GCSE · Chapter 17
Waves: transverse, longitudinal and wave speed
By the end of this chapter you will be able to
- Classify waves as transverse or longitudinal, and explain the direction of vibration
- Label a wave diagram with amplitude and wavelength, and find the period from the frequency
- Calculate wave speed, frequency or wavelength using v = f lambda
- Calculate the distance from an echo time, and explain ultrasound uses
You should already know
- Energy transfers by waves (Chapter 1)
- Speed, distance and time (Chapter 16)
Where this leads
- Reflection, refraction and lenses (Chapter 18)
- The electromagnetic spectrum (Chapter 19)
GCSE Physics. Content follows the GCSE (9-1) subject content for England (Edexcel and AQA). Content references: Distinguish transverse and longitudinal waves, with examples, and the direction of vibration, Describe amplitude, wavelength, frequency (in hertz) and period, and use T = 1 / f, Use the wave equation v = f lambda, Describe reflection and refraction of waves at a boundary (idea only), Describe sound as a longitudinal wave, its speed in air, ultrasound uses, and measuring the speed of sound by echo.
Exercise P Do you remember?
1
FWhat is 5 x 2? Write the number.
10
Method. Multiply.
- Multiply. 5 x 2 = 10.10
- Write the answer. 10
Check. ✓
2
FWhat is 1 divided by 50? Write the number as a decimal.
0.02
Method. Divide.
- Divide. 1 / 50 = 0.02.0.02
- Write the answer. 0.02
Check. ✓
3
FWhat is 340 divided by 2? Write the number.
170
Method. Divide.
- Divide. 340 / 2 = 170.170
- Write the answer. 170
Check. ✓
4
RWhich way does energy travel in a wave, relative to the vibration? Write the word: along or across.
along
Method. Think about the direction of travel.
- Recall. The energy travels along the wave, while the particles vibrate.along
- Write the answer. along
Check. ✓
5
FWhat is the unit of frequency? Write the unit.
hertz
Method. Recall the unit.
- Recall. Frequency is measured in hertz, Hz.hertz (Hz)
- Write the answer. hertz
Check. ✓
17.1
Transverse and longitudinal waves
Video lesson: Transverse and longitudinal wavesComing soon
Context. A stone is dropped into a pond, and ripples spread out. A leaf on the water bobs up and down but does not travel with the ripples. The ripples carry energy outwards, but the water itself only moves up and down. This is a transverse wave.
A wave transfers energy from one place to another without transferring matter. There are two main types:
- Transverse: the vibration is at right angles to the direction the wave travels. Examples: water ripples, light, and other electromagnetic waves, and waves on a rope.
- Longitudinal: the vibration is along the direction the wave travels. The wave has compressions (crowded particles) and rarefactions (spread-out particles). Examples: sound waves in air, and some waves in a slinky.
Transverse wave: vibration up and down, travel to the right
Longitudinal wave: vibration along the direction of travel
Key ideas
- Transverse: vibration at right angles to the direction of travel.
- Longitudinal: vibration along the direction of travel.
- Examples of transverse: light, water ripples, electromagnetic waves.
- Examples of longitudinal: sound waves in air, waves in a slinky spring.
Worked example 17.1.1
Light is a transverse wave. Which way do the vibrations point compared with the direction of travel? Write the word: parallel or perpendicular.
Method. Recall the definition of a transverse wave.
- Recall. In a transverse wave the vibration is at right angles to the travel.at right angles
- Decide. So the vibrations are perpendicular to the direction of travel.perpendicular
- Write the answer. perpendicular
Check. ✓
Worked example 17.1.2
Sound in air is a longitudinal wave. Write the word that describes the crowded parts of the wave.
Method. Recall the name of the crowded part.
- Look. The crowded regions are where the particles are pushed together.crowded
- Recall. The crowded parts of a longitudinal wave are compressions.compressions
- Write the answer. compressions
Check. The spread-out parts are rarefactions. ✓
Worked example 17.1.3
Which type of wave has vibrations at right angles to the direction of travel: transverse or longitudinal? Write the word.
Method. Recall the definition.
- Look. In one type of wave, the vibrations are at right angles to the travel.right angles
- Decide. That type is transverse.transverse
- Write the answer. transverse
Check. ✓
Watch out
Watch out: in both types of wave, the particles do not travel with the wave. They vibrate about a fixed position, and the energy moves on.
Exam tip
Exam tip. Say “at right angles” for transverse and “along the direction of travel” for longitudinal. Both phrases score.
Exercise 17A Types of wave
1
FWhich type of wave has vibrations at right angles to the direction of travel? Write the word: transverse or longitudinal.
transverse
Method. Recall the definition.
- Recall. Transverse waves vibrate at right angles to the direction of travel.transverse
- Write the answer. transverse
Check. ✓
2
FWhich type of wave has vibrations along the direction of travel? Write the word: transverse or longitudinal.
longitudinal
Method. Recall the definition.
- Recall. Longitudinal waves vibrate along the direction of travel.longitudinal
- Write the answer. longitudinal
Check. ✓
3
FName a transverse wave. Write the name.
light
Method. Recall an example.
- Recall. Light is a transverse electromagnetic wave.light
- Write the answer. light
Check. Accept water waves, or other electromagnetic waves. ✓
4
FName a longitudinal wave. Write the name.
sound
Method. Recall an example.
- Recall. Sound in air is a longitudinal wave.sound
- Write the answer. sound
Check. Accept a wave in a slinky. ✓
5
FIn a longitudinal wave, what are the crowded regions called? Write the word.
compressions
Method. Recall the name.
- Recall. The crowded regions are compressions.compressions
- Write the answer. compressions
Check. ✓
6
FIn a longitudinal wave, what are the spread-out regions called? Write the word.
rarefactions
Method. Recall the name.
- Recall. The spread-out regions are rarefactions.rarefactions
- Write the answer. rarefactions
Check. ✓
7
FDo the particles of a water wave travel from the source to the shore? Write yes or no.
no
Method. The particles vibrate about fixed positions.
- Recall. The water particles move up and down; the energy moves to the shore.no
- Write the answer. no
Check. ✓
8
FWhich type of wave is a slinky spring when it is pushed along its length? Write the word.
longitudinal
Method. The coils move along the spring.
- Recall. The coils vibrate along the direction of the spring, which is longitudinal.longitudinal
- Write the answer. longitudinal
Check. ✓
9
FWhich type of wave is a wave on a rope that is shaken up and down? Write the word.
transverse
Method. The rope moves at right angles to the travel.
- Recall. The rope vibrates up and down, at right angles to the direction of travel.transverse
- Write the answer. transverse
Check. ✓
10
RExplain in one sentence why a sound wave is longitudinal. Accept any sentence that says the air particles vibrate along the direction the sound travels.
Accept any sentence that says the air particles vibrate along the direction the sound travels.
Method. Think about the particles.
- Particles. The air particles are pushed and pulled along the direction of travel.along
- Waves. So the wave is longitudinal.longitudinal
- Write the answer. Accept any sentence that says the air particles vibrate along the direction the sound travels.
Check. ✓
11
RA pupil says “a wave carries matter from one place to another.” Explain why this is wrong, in one sentence. Accept any sentence that says waves transfer energy, not matter.
Accept any sentence that says waves transfer energy, not matter.
Method. Think about what moves.
- Matter. The particles only vibrate about their positions.vibrate
- Energy. Waves transfer energy, not matter.energy
- Write the answer. Accept any sentence that says waves transfer energy, not matter.
Check. ✓
12
RGive one difference between transverse and longitudinal waves in the direction of vibration. Accept any sentence that says transverse vibrations are at right angles and longitudinal ones are along the travel.
Accept any sentence that says transverse vibrations are at right angles and longitudinal ones are along the travel.
Method. Compare the directions.
- Transverse. Transverse: at right angles to the travel.right angles
- Longitudinal. Longitudinal: along the travel.along
- Write the answer. Accept any sentence that says transverse vibrations are at right angles and longitudinal ones are along the travel.
Check. ✓
17.2
Amplitude, wavelength, frequency and period
Video lesson: Amplitude, wavelength, frequency and periodComing soon
Context. A ripple tank is set up by the teacher. The wave maker vibrates ten times each second. The class measures how far apart the waves are, and how tall they are.
The amplitude is the maximum displacement from the rest position. The wavelength (lambda) is the distance from one point on a wave to the same point on the next wave, such as crest to crest. The frequency is the number of waves passing a point each second, in hertz (Hz). The period is the time for one complete wave, and it is the inverse of the frequency:
T = 1 / f, so f = 1 / T
Amplitude and wavelength on a transverse wave
| Quantity | Symbol | Unit |
|---|---|---|
| amplitude | A | metre (m), the maximum displacement from the rest position |
| wavelength | lambda | metre (m), from one point to the same point on the next wave |
| frequency | f | hertz (Hz), waves per second |
| period | T | second (s), the time for one complete wave |
| wave speed | v | metre per second (m/s) |
Quantities used to describe waves
Key ideas
- Amplitude: height from rest to crest.
- Wavelength: crest to crest (or any point to the same point on the next wave).
- Frequency f in hertz: waves per second.
- Period T = 1 / f, in seconds.
Worked example 17.2.1
A wave has a frequency of 50 Hz. Calculate its period. Write the number of seconds.
Method. Use T = 1 / f.
- Take the numbers. f = 50 Hz.f = 50
- Divide. T = 1 / 50 = 0.02 s.1 / 50 = 0.02
- Write the answer. 0.02 s
Check. 1 / 0.02 = 50 Hz. ✓
Worked example 17.2.2
A wave has a period of 0.25 s. Calculate its frequency. Write the number of hertz.
Method. Use f = 1 / T.
- Take the numbers. T = 0.25 s.T = 0.25
- Divide. f = 1 / 0.25 = 4 Hz.1 / 0.25 = 4
- Write the answer. 4 Hz
Check. ✓
Worked example 17.2.3
In the diagram, one complete wave is 2 cm long. What is the wavelength? Write the number of cm.
Method. The wavelength is the length of one complete wave.
- Read. One complete wave spans 2 cm, from crest to the next crest.2 cm
- Decide. So the wavelength is 2 cm.2 cm
- Write the answer. 2 cm
Check. ✓
Watch out
Watch out: amplitude is the height from the rest position to a crest, not the whole height from trough to crest.
Exam tip
Exam tip. Give frequency in hertz and period in seconds. A higher frequency gives a shorter period.
Exercise 17B Amplitude, wavelength, frequency and period
1
FWhat is the unit of frequency? Write the unit.
hertz
Method. Recall the unit.
- Recall. Frequency is measured in hertz, Hz.Hz
- Write the answer. hertz (Hz)
Check. ✓
2
FWhat does the amplitude of a wave describe? Write one word: height or speed.
height
Method. Recall the definition.
- Recall. The amplitude is the maximum height from the rest position.height
- Write the answer. height
Check. ✓
3
FA wave has a frequency of 10 Hz. How many waves pass a point in 1 second? Write the number.
10
Method. Frequency is waves per second.
- Recall. A frequency of 10 Hz is 10 waves per second.10
- Write the answer. 10
Check. ✓
4
FA wave has a frequency of 4 Hz. Calculate the period. Write the number of seconds.
0.25
Method. T = 1 / f.
- Divide. T = 1 / 4 = 0.25 s.1 / 4 = 0.25
- Write the answer. 0.25 s
Check. ✓
5
FA wave has a period of 0.5 s. Calculate its frequency. Write the number of hertz.
2
Method. f = 1 / T.
- Divide. f = 1 / 0.5 = 2 Hz.1 / 0.5 = 2
- Write the answer. 2 Hz
Check. ✓
6
PSA wave has a frequency of 200 Hz. Calculate the period. Write the number of seconds.
0.005
Method. T = 1 / f.
- Divide. T = 1 / 200 = 0.005 s.1 / 200 = 0.005
- Write the answer. 0.005 s
Check. ✓
7
PSA wave has a period of 0.001 s. What is its frequency? Write the number of hertz.
1000
Method. f = 1 / T.
- Divide. f = 1 / 0.001 = 1000 Hz.1 / 0.001 = 1000
- Write the answer. 1000 Hz
Check. ✓
8
PSA wave has a wavelength of 4 cm. How long, in cm, are two complete waves laid end to end? Write the number of cm.
8
Method. Each wave is 4 cm long.
- Multiply. Two wavelengths = 2 x 4 = 8 cm.2 x 4 = 8
- Write the answer. 8 cm
Check. ✓
9
RTwo waves have the same amplitude but different wavelengths. Do they necessarily have the same frequency? Write yes or no.
no
Method. Amplitude and wavelength are separate properties.
- Check. Amplitude does not fix frequency, and different wavelengths give different frequencies at a set speed.no
- Write the answer. no
Check. ✓
10
RExplain why the period of a wave is the time for one complete wave, in one sentence. Accept any sentence that says it is the time for one full wave to pass a point, which is the inverse of the frequency.
Accept any sentence that says it is the time for one full wave to pass a point, which is the inverse of the frequency.
Method. Think about what frequency counts.
- Frequency. Frequency counts the waves per second.per second
- Period. So the period is the time for one wave, the inverse of the frequency.inverse
- Write the answer. Accept any sentence that says it is the time for one full wave to pass a point, which is the inverse of the frequency.
Check. ✓
11
RA pupil says “doubling the frequency doubles the period.” Explain why this is wrong. Accept any answer that says doubling the frequency halves the period, since T = 1 / f.
Accept any answer that says doubling the frequency halves the period, since T = 1 / f.
Method. Use T = 1 / f.
- Halve. If f doubles, then 1 / f is halved.halved
- Link. So the period is halved, not doubled.halved
- Write the answer. Accept any answer that says doubling the frequency halves the period, since T = 1 / f.
Check. ✓
17.3
The wave equation: v = f lambda
Video lesson: The wave equation: v = f lambdaComing soon
Context. A water wave in a tank travels a set distance in a set time. The teacher says: “If the frequency doubles, what happens to the wavelength?” The wave equation answers this.
The speed of a wave is the frequency multiplied by the wavelength:
v = f x lambda, with v in m/s, f in Hz and lambda in m
The equation can be rearranged: f = v / lambda and lambda = v / f. For a given wave speed, a higher frequency gives a shorter wavelength.
Key ideas
- v = f x lambda. Speed in m/s, frequency in Hz, wavelength in m.
- lambda = v / f; f = v / lambda.
- For a fixed speed, higher frequency means shorter wavelength.
- Convert cm to m before you calculate.
Worked example 17.3.1
A wave has a frequency of 5 Hz and a wavelength of 2 m. Calculate the wave speed. Write the number of m/s.
Method. Use v = f x lambda.
- Take the numbers. f = 5 Hz and lambda = 2 m.f = 5, lambda = 2
- Multiply. v = 5 x 2 = 10 m/s.5 x 2 = 10
- Write the answer. 10 m/s
Check. 10 / 5 = 2 m. ✓
Worked example 17.3.2
A wave travels at 0.2 m/s, with a frequency of 4 Hz. Find the wavelength. Write the number of metres.
Method. Use lambda = v / f.
- Take the numbers. v = 0.2 m/s and f = 4 Hz.v = 0.2, f = 4
- Divide. lambda = 0.2 / 4 = 0.05 m.0.2 / 4 = 0.05
- Write the answer. 0.05 m
Check. 4 x 0.05 = 0.2 m/s. ✓
Worked example 17.3.3
A sound wave has a speed of 340 m/s and a frequency of 170 Hz. Find its wavelength. Write the number of metres.
Method. Use lambda = v / f.
- Take the numbers. v = 340 m/s and f = 170 Hz.v = 340, f = 170
- Divide. lambda = 340 / 170 = 2 m.340 / 170 = 2
- Write the answer. 2 m
Check. 170 x 2 = 340 m/s. ✓
Watch out
Watch out: convert the wavelength from cm to m before you substitute. 50 cm is 0.5 m.
Exam tip
Exam tip. Write v = f lambda, and then rearrange to the quantity you need. Check that the units work out.
Exercise 17C The wave equation
1
FWrite the wave equation in words: speed = frequency x ... Write the missing word.
wavelength
Method. Recall the wave equation.
- Recall. The wave equation is v = f lambda, so speed = frequency x wavelength.wavelength
- Write the answer. wavelength
Check. ✓
2
FA wave has a frequency of 3 Hz and a wavelength of 4 m. Calculate the speed. Write the number of m/s.
12
Method. Use v = f lambda.
- Multiply. v = 3 x 4 = 12 m/s.3 x 4 = 12
- Write the answer. 12 m/s
Check. ✓
3
FA wave travels at 20 m/s with a wavelength of 5 m. Calculate the frequency. Write the number of hertz.
4
Method. Use f = v / lambda.
- Divide. f = 20 / 5 = 4 Hz.20 / 5 = 4
- Write the answer. 4 Hz
Check. ✓
4
FA wave travels at 30 m/s at 6 Hz. Calculate the wavelength. Write the number of metres.
5
Method. Use lambda = v / f.
- Divide. lambda = 30 / 6 = 5 m.30 / 6 = 5
- Write the answer. 5 m
Check. ✓
5
PSA wave has a wavelength of 0.5 m and a speed of 100 m/s. Calculate the frequency. Write the number of hertz.
200
Method. Use f = v / lambda.
- Divide. f = 100 / 0.5 = 200 Hz.100 / 0.5 = 200
- Write the answer. 200 Hz
Check. ✓
6
PSA wave has a wavelength of 50 cm and a frequency of 8 Hz. Calculate the speed in m/s. Write the number.
4
Method. Convert 50 cm to 0.5 m, then v = f lambda.
- Convert. 50 cm = 0.5 m.0.5 m
- Multiply. v = 8 x 0.5 = 4 m/s.8 x 0.5 = 4
- Write the answer. 4 m/s
Check. ✓
7
PSA wave has a speed of 340 m/s and a frequency of 34 Hz. Calculate the wavelength. Write the number of metres.
10
Method. Use lambda = v / f.
- Divide. lambda = 340 / 34 = 10 m.340 / 34 = 10
- Write the answer. 10 m
Check. ✓
8
RTwo waves travel at the same speed. Wave A has twice the frequency of wave B. What is the ratio of the wavelength of A to B? Write the number.
0.5
Method. For the same speed, lambda is proportional to 1 / f.
- Ratio. lambda A = v / 2f and lambda B = v / f, so lambda A / lambda B = 1/2 = 0.5.0.5
- Write the answer. 0.5
Check. ✓
9
PSA wave has a frequency of 400 Hz and a speed of 340 m/s. Calculate the wavelength in cm. Write the number of cm.
85
Method. Find lambda in m, then convert to cm.
- Divide. lambda = 340 / 400 = 0.85 m.0.85
- Convert. 0.85 m = 85 cm.85
- Write the answer. 85 cm
Check. ✓
10
PSA water wave has a wavelength of 3 cm and a frequency of 5 Hz. What is the wave speed in cm/s? Write the number.
15
Method. Use v = f lambda in cm and Hz.
- Multiply. v = 5 x 3 = 15 cm/s.5 x 3 = 15
- Write the answer. 15 cm/s
Check. ✓
11
RExplain why a higher frequency gives a shorter wavelength if the speed is the same, in one sentence. Accept any sentence that says lambda = v / f, so a larger f gives a smaller lambda.
Accept any sentence that says lambda = v / f, so a larger f gives a smaller lambda.
Method. Look at lambda = v / f.
- Equation. lambda = v / f, with v fixed.v / f
- Result. A larger f makes the divisor bigger, so lambda is smaller.smaller
- Write the answer. Accept any sentence that says lambda = v / f, so a larger f gives a smaller lambda.
Check. ✓
17.4
Reflection and refraction of waves (idea)
Video lesson: Reflection and refraction of waves (idea)Coming soon
Context. In a ripple tank, the waves hit the edge of the tank and bounce back. When the water is shallow on one side, the waves change direction as they cross into it. These are reflection and refraction, and they happen to all waves.
Reflection: a wave bounces back when it meets a boundary, with the angle of reflection equal to the angle of incidence. Refraction: a wave changes direction when it passes from one medium into another where its speed changes. When the wave slows down (for example, moving from deep to shallow water), it bends towards the normal. The frequency stays the same, but the wavelength changes.
Key ideas
- Reflection: the wave bounces back from a boundary.
- Refraction: the wave changes direction when its speed changes at a boundary.
- Refraction: the frequency stays the same; the wavelength and speed change.
- A wave slowing down bends towards the normal.
Worked example 17.4.1
A water wave slows down as it passes into shallow water. Does its frequency change? Write yes or no.
Method. The frequency is set by the source.
- Recall. The frequency of a wave stays the same at a boundary.no
- Change. The wave speed and wavelength change instead.speed and wavelength
- Write the answer. no
Check. ✓
Worked example 17.4.2
A wave is reflected at a flat boundary. If the angle of incidence is 30 degrees, what is the angle of reflection? Write the number of degrees.
Method. The angle of reflection equals the angle of incidence.
- Look. The boundary is flat, so the law of reflection applies.law of reflection
- Recall. Angle of reflection = angle of incidence = 30 degrees.30
- Write the answer. 30 degrees
Check. ✓
Worked example 17.4.3
A ray hits a flat mirror at 40 degrees to the normal. What is the angle of reflection? Write the number of degrees.
Method. Use the law of reflection.
- Look. The angle is measured from the normal, which is at right angles to the surface.normal
- Recall. The angle of reflection equals the angle of incidence: 40 degrees.40
- Write the answer. 40 degrees
Check. ✓
Watch out
Watch out: at a boundary, the frequency does not change. Only the speed and the wavelength change in refraction.
Exam tip
Exam tip. When describing refraction, say which way the wave bends, and whether it is slowing down or speeding up.
Exercise 17D Reflection and refraction
1
FWhat is the name of the process when a wave bounces off a boundary? Write the word.
reflection
Method. Recall the process.
- Recall. Bouncing back from a boundary is reflection.reflection
- Write the answer. reflection
Check. ✓
2
FWhat is the name of the process when a wave changes direction at a boundary because its speed changes? Write the word.
refraction
Method. Recall the process.
- Recall. Changing direction when the speed changes is refraction.refraction
- Write the answer. refraction
Check. ✓
3
FWhen a wave is reflected, is the angle of reflection equal to or different from the angle of incidence? Write equal or different.
equal
Method. The law of reflection.
- Recall. The angle of reflection equals the angle of incidence.equal
- Write the answer. equal
Check. ✓
4
FA wave travels from deep water into shallow water. Does its speed increase or decrease? Write the word.
decrease
Method. Shallow water slows waves.
- Recall. The wave slows down in shallow water.decrease
- Write the answer. decrease
Check. ✓
5
FIn refraction, does the frequency of the wave change? Write yes or no.
no
Method. Frequency is set by the source.
- Recall. The frequency stays the same; the speed and wavelength change.no
- Write the answer. no
Check. ✓
6
FA wave slows down on crossing a boundary. Which way does it bend: towards or away from the normal? Write towards or away.
towards
Method. A slower wave bends towards the normal.
- Recall. When a wave slows down, it bends towards the normal.towards
- Write the answer. towards
Check. ✓
7
FThe angle of incidence is 45 degrees. What is the angle of reflection? Write the number of degrees.
45
Method. Angle of reflection equals angle of incidence.
- Recall. The angle of reflection is 45 degrees.45
- Write the answer. 45 degrees
Check. ✓
8
PSA wave changes from speed 0.4 m/s to 0.2 m/s at a boundary, with frequency 4 Hz. What is the wavelength after the boundary? Write the number of metres.
0.05
Method. Use lambda = v / f with the new speed.
- Divide. lambda = 0.2 / 4 = 0.05 m.0.2 / 4 = 0.05
- Write the answer. 0.05 m
Check. ✓
9
RExplain in one sentence why a wave bends when it enters a new material at an angle. Accept any sentence that says the speed of the wave changes in the new material, so it changes direction.
Accept any sentence that says the speed of the wave changes in the new material, so it changes direction.
Method. Think about the speed.
- Speed. The wave speed changes at the boundary.speed changes
- Direction. So one side of the wave changes speed first, and the wave changes direction.direction
- Write the answer. Accept any sentence that says the speed of the wave changes in the new material, so it changes direction.
Check. ✓
10
RA pupil says “refraction changes the frequency of the wave.” Explain why this is wrong, in one sentence. Accept any sentence that says the frequency is set by the source and does not change at a boundary.
Accept any sentence that says the frequency is set by the source and does not change at a boundary.
Method. Think about the source.
- Source. The frequency is set by the source of the wave.source
- Boundary. It does not change at a boundary, only the speed and wavelength do.does not change
- Write the answer. Accept any sentence that says the frequency is set by the source and does not change at a boundary.
Check. ✓
11
PSIn a ripple tank, a wave hits a straight barrier and bounces back. Name the process. Write the word.
reflection
Method. The wave bounces off the barrier.
- Recall. Bouncing off a barrier is reflection.reflection
- Write the answer. reflection
Check. ✓
17.5
Sound, ultrasound and measuring the speed of sound
Video lesson: Sound, ultrasound and measuring the speed of soundComing soon
Context. A driver sounds a horn at a wall and the echo comes back after a short time. The teacher asks the class to find how far away the wall is, from the time of the echo. The speed of sound in air is needed for this calculation.
Sound is a longitudinal wave. In air, sound travels at about 340 m/s. Sound with a frequency above about 20 000 Hz is called ultrasound. Ultrasound is used in medicine (scans), in sonar and depth finding, and in cleaning. It is used because it reflects from boundaries inside objects and does not use harmful ionising radiation.
To measure the distance to a wall by echo, measure the time between the sound being made and the echo returning. The sound travels to the wall and back, so the total distance is twice the distance to the wall:
distance to the wall = speed x time / 2
Measuring distance by echo: the sound travels there and back
| Use | Wave | Why |
|---|---|---|
| ultrasound scan of a baby | ultrasound (above 20 kHz) | reflects from boundaries inside the body; no harmful ionising radiation |
| sonar or depth finding | ultrasound or sound | echo time gives the distance |
| cleaning jewellery | ultrasound | vibrates dirt off the surface |
| ripple tank | water waves | shows reflection and refraction of waves |
Uses of ultrasound and echoes
Key ideas
- Sound is longitudinal; its speed in air is about 340 m/s.
- Ultrasound: sound above 20 000 Hz.
- Echo: distance to the reflector = speed x time / 2.
- Ultrasound is used in scans because it reflects from boundaries inside the body.
Worked example 17.5.1
A sound echo returns after 2 s from a wall. The speed of sound is 340 m/s. How far away is the wall? Write the number of metres.
Method. The sound travels there and back, so use distance = speed x time / 2.
- Total. Total distance = 340 x 2 = 680 m.340 x 2 = 680
- Halve. Distance to the wall = 680 / 2 = 340 m.680 / 2 = 340
- Write the answer. 340 m
Check. ✓
Worked example 17.5.2
An ultrasound pulse takes 0.0001 s to return from a reflector in the body. The speed of ultrasound is 1500 m/s in tissue. Find the distance to the reflector. Write the number of metres.
Method. Use distance = speed x time / 2.
- Multiply. Total = 1500 x 0.0001 = 0.15 m.1500 x 0.0001 = 0.15
- Halve. Distance = 0.15 / 2 = 0.075 m.0.15 / 2 = 0.075
- Write the answer. 0.075 m
Check. ✓
Worked example 17.5.3
An echo returns after 4 s from a wall, with sound at 340 m/s. How far away is the wall? Write the number of metres.
Method. Use distance = speed x time / 2.
- Total. Total path = 340 x 4 = 1360 m.1360
- Halve. Distance to the wall = 1360 / 2 = 680 m.680
- Write the answer. 680 m
Check. ✓
Watch out
Watch out: the sound goes to the wall and back. Always halve the total distance to find the distance to the wall.
Exam tip
Exam tip. Write the total path (speed x time), then halve it. A missing halving is the most common mistake in echo questions.
Exercise 17E Sound, ultrasound and echoes
1
FWhat is the approximate speed of sound in air? Write the number of m/s.
340
Method. Recall the value.
- Recall. The speed of sound in air is about 340 m/s.340
- Write the answer. 340 m/s
Check. ✓
2
FWhat is the frequency range that is called ultrasound (above which value)? Write the number of hertz.
20000
Method. Recall the limit.
- Recall. Ultrasound is sound above about 20 000 Hz.20 000
- Write the answer. 20 000 Hz
Check. ✓
3
FWhich type of wave is sound in air? Write the word: transverse or longitudinal.
longitudinal
Method. Recall the type.
- Recall. Sound in air is a longitudinal wave.longitudinal
- Write the answer. longitudinal
Check. ✓
4
PSAn echo returns after 1 s from a wall. How far away is the wall? Write the number of metres. (Use 340 m/s.)
170
Method. Distance = speed x time / 2.
- Multiply. Total = 340 x 1 = 340 m.340
- Halve. Distance = 340 / 2 = 170 m.170
- Write the answer. 170 m
Check. ✓
5
PSAn echo returns after 0.5 s from a cliff. How far is the cliff? Write the number of metres. (Use 340 m/s.)
85
Method. Distance = speed x time / 2.
- Multiply. Total = 340 x 0.5 = 170 m.170
- Halve. Distance = 170 / 2 = 85 m.85
- Write the answer. 85 m
Check. ✓
6
RA scan uses ultrasound. Name one reason ultrasound is used in medical scans. Write one reason in a few words. Accept any reason such as reflects from body boundaries or no ionising radiation.
Accept any reason such as reflects from body boundaries or no ionising radiation.
Method. Think about what ultrasound does in the body.
- Reflects. Ultrasound reflects from boundaries inside the body.reflects
- Safe. It does not use ionising radiation.no ionising radiation
- Write the answer. Accept any reason such as reflects from body boundaries or no ionising radiation.
Check. ✓
7
RExplain why ultrasound is used for scanning rather than X-rays for an unborn baby, in one sentence. Accept any sentence that says ultrasound does not use ionising radiation, so it is safer.
Accept any sentence that says ultrasound does not use ionising radiation, so it is safer.
Method. Compare the two waves.
- Ultrasound. Ultrasound is a sound wave with no ionising radiation.no ionising
- Safety. So it is safer for the baby than X-rays.safer
- Write the answer. Accept any sentence that says ultrasound does not use ionising radiation, so it is safer.
Check. ✓
8
PSA ship sends an ultrasound pulse down to the sea floor and receives the echo after 0.6 s. The speed of ultrasound in sea water is 1500 m/s. How deep is the sea? Write the number of metres.
450
Method. Total path = speed x time, then halve it.
- Total. Total = 1500 x 0.6 = 900 m.900
- Halve. Depth = 900 / 2 = 450 m.450
- Write the answer. 450 m
Check. ✓
9
RExplain why the echo method uses half of the total distance travelled by the sound, in one sentence. Accept any sentence that says the sound travels to the reflector and back.
Accept any sentence that says the sound travels to the reflector and back.
Method. Think about the path.
- Path. The sound goes to the reflector and returns.there and back
- Half. So the distance to the reflector is half of the total path.half
- Write the answer. Accept any sentence that says the sound travels to the reflector and back.
Check. ✓
10
PSAn echo returns after 0.2 s from a wall. Using 340 m/s, find the distance to the wall. Write the number of metres.
34
Method. Total path first, then halve.
- Total. Total path = 340 x 0.2 = 68 m.68
- Halve. Distance = 68 / 2 = 34 m.68 / 2 = 34
- Write the answer. 34 m
Check. ✓
Chapter summary
| Skill | Method |
|---|---|
| Transverse and longitudinal | Transverse: vibration at right angles; longitudinal: vibration along the travel |
| Describe a wave | Amplitude (height); wavelength (repeat distance); frequency (Hz); period T = 1 / f |
| Wave equation | v = f lambda; lambda = v / f; f = v / lambda |
| Reflection and refraction | Reflection bounces back; refraction changes direction when speed changes; frequency unchanged |
| Sound and echoes | Sound about 340 m/s in air; distance = speed x time / 2; ultrasound above 20 000 Hz |
Can you…?
- I can tell transverse and longitudinal waves apart
- I can describe amplitude, wavelength, frequency and period
- I can calculate speed, frequency and wavelength using v = f lambda
- I can explain reflection and refraction at a boundary
- I can calculate the distance from an echo time, and explain ultrasound uses
Key terms
- transverse wave
- a wave whose vibration is at right angles to the direction of travel
- longitudinal wave
- a wave whose vibration is along the direction of travel
- amplitude
- the maximum displacement from the rest position
- wavelength
- the distance from one point on a wave to the same point on the next wave
- frequency
- the number of waves passing a point each second, in hertz (Hz)
- period
- the time for one complete wave, T = 1 / f
- ultrasound
- sound with a frequency above about 20 000 Hz
Exercise 17Z Check-up
1
What type of wave has vibrations along the direction of travel? Write the word.
longitudinal
Method. Recall.
- Recall. Longitudinal waves vibrate along the direction of travel.longitudinal
- Write the answer. longitudinal
Check. ✓
2
Calculate the period of a 25 Hz wave. Write the number of seconds.
0.04
Method. T = 1 / f.
- Divide. T = 1 / 25 = 0.04 s.1 / 25 = 0.04
- Write the answer. 0.04 s
Check. ✓
3
A wave has a frequency of 6 Hz and a wavelength of 2 m. Calculate its speed. Write the number of m/s.
12
Method. v = f lambda.
- Multiply. v = 6 x 2 = 12 m/s.6 x 2 = 12
- Write the answer. 12 m/s
Check. ✓
4
A wave travels at 10 m/s with a frequency of 5 Hz. Calculate the wavelength. Write the number of metres.
2
Method. lambda = v / f.
- Divide. lambda = 10 / 5 = 2 m.10 / 5 = 2
- Write the answer. 2 m
Check. ✓
5
What is the amplitude of a wave? Write one word: height or length.
height
Method. Recall.
- Recall. The amplitude is the maximum height from the rest position.height
- Write the answer. height
Check. ✓
6
Name the process when a wave bounces off a surface. Write the word.
reflection
Method. Recall.
- Recall. Bouncing off a surface is reflection.reflection
- Write the answer. reflection
Check. ✓
7
Calculate the distance to a wall when an echo returns after 3 s, using 340 m/s. Write the number of metres.
510
Method. Distance = speed x time / 2.
- Multiply. 340 x 3 = 1020 m.1020
- Halve. 1020 / 2 = 510 m.510
- Write the answer. 510 m
Check. ✓
8
What is the speed of sound in air, approximately? Write the number of m/s.
340
Method. Recall.
- Recall. The speed of sound in air is about 340 m/s.340
- Write the answer. 340 m/s
Check. ✓
9
Does refraction change the frequency of a wave at a boundary? Write yes or no.
no
Method. Frequency is set by the source.
- Recall. Refraction changes the speed and wavelength, not the frequency.no
- Write the answer. no
Check. ✓
10
Explain why a longitudinal wave has compressions and rarefactions, in one sentence. Accept any sentence that says the particles are pushed together and spread apart along the direction of travel.
Accept any sentence that says the particles are pushed together and spread apart along the direction of travel.
Method. Think about the particles.
- Push. The vibration pushes particles together and then apart.together and apart
- Write the answer. Accept any sentence that says the particles are pushed together and spread apart along the direction of travel.
Check. ✓
Total 29 marks. Allow about 29 minutes.
Exercise 17X Exam-style questions
1
FA wave has a period of 0.02 s. Calculate its frequency. Write the number of hertz.[2 marks]
50
Method. f = 1 / T.
- Divide. f = 1 / 0.02 = 50 Hz.1 / 0.02 = 50
- Write the answer. 50 Hz
Check. ✓
2
FA wave has a frequency of 8 Hz and a wavelength of 1.5 m. Calculate the wave speed. Write the number of m/s.[2 marks]
12
Method. v = f lambda.
- Multiply. v = 8 x 1.5 = 12 m/s.8 x 1.5 = 12
- Write the answer. 12 m/s
Check. ✓
3
FClassify the waves: light, sound in air, and a wave on a rope shaken up and down. Write the three types, transverse or longitudinal, in order, separated by commas.[2 marks]
transverse, longitudinal, transverse
Method. Recall each type.
- Light. Light is transverse.transverse
- Sound. Sound in air is longitudinal.longitudinal
- Rope. A rope shaken up and down is transverse.transverse
- Write the answer. transverse, longitudinal, transverse
Check. ✓
4
RDescribe the difference between transverse and longitudinal waves, using the direction of vibration and an example of each. Accept any answer that says transverse vibrations are at right angles (e.g. light) and longitudinal vibrations are along the direction of travel (e.g. sound).[4 marks]
Accept any answer that says transverse vibrations are at right angles (e.g. light) and longitudinal vibrations are along the direction of travel (e.g. sound).
Method. Compare the two types.
- Transverse. Transverse: the vibration is at right angles to the direction of travel, for example light.right angles
- Longitudinal. Longitudinal: the vibration is along the direction of travel, for example sound.along
- Energy. Both types transfer energy without transferring matter.energy
- Write the answer. Accept any answer that says transverse vibrations are at right angles (e.g. light) and longitudinal vibrations are along the direction of travel (e.g. sound).
Check. ✓
5
PSA water wave has a wavelength of 0.04 m and a frequency of 25 Hz. Calculate the wave speed. Write the number of m/s.[3 marks]
1
Method. Use v = f lambda.
- Multiply. v = 25 x 0.04 = 1 m/s.25 x 0.04 = 1
- Write the answer. 1 m/s
Check. ✓
6
PSA sound wave has a frequency of 440 Hz and travels at 340 m/s in air. Calculate its wavelength in metres to 2 decimal places. Write the number.[3 marks]
0.77
Method. Use lambda = v / f.
- Divide. lambda = 340 / 440 = 0.7727... m, which is 0.77 m to 2 decimal places.340 / 440 = 0.77
- Write the answer. 0.77 m
Check. ✓
7
PSAn echo from a wall returns after 4 s. Calculate the distance to the wall, using 340 m/s. Write the number of metres.[3 marks]
680
Method. Total path first, then halve.
- Total. Total path = 340 x 4 = 1360 m.1360
- Halve. Distance = 1360 / 2 = 680 m.680
- Write the answer. 680 m
Check. ✓
8
RExplain how ultrasound is used to measure the depth of the sea. Accept any answer that says a pulse is sent down, the echo time is measured, and the depth is half of speed times time.[4 marks]
Accept any answer that says a pulse is sent down, the echo time is measured, and the depth is half of speed times time.
Method. Describe the method.
- Pulse. An ultrasound pulse is sent down to the sea floor.pulse
- Echo. The time for the echo to return is measured.time
- Calculate. Depth = speed x time / 2, using the speed of ultrasound in water.speed x time / 2
- Reason. Halving is needed because the pulse travels down and back.halve
- Write the answer. Accept any answer that says a pulse is sent down, the echo time is measured, and the depth is half of speed times time.
Check. ✓
9
RExplain how the frequency and the wavelength of a wave are linked when the speed is fixed, and say what happens to the wavelength when the frequency is doubled. Accept any answer that says lambda = v / f, so doubling f halves the wavelength.[3 marks]
Accept any answer that says lambda = v / f, so doubling f halves the wavelength.
Method. Use the wave equation.
- Equation. v = f lambda, so lambda = v / f.lambda = v / f
- Doubling. If f doubles with v fixed, lambda halves.halves
- Write the answer. Accept any answer that says lambda = v / f, so doubling f halves the wavelength.
Check. ✓
10
RA wave enters water from air at an angle. Describe what happens to its speed, wavelength and frequency, if it slows down. Accept any answer that says the speed and wavelength decrease, and the frequency stays the same.[3 marks]
Accept any answer that says the speed and wavelength decrease, and the frequency stays the same.
Method. Think about each quantity.
- Speed. The speed decreases as the wave slows.decreases
- Wavelength. The wavelength decreases because lambda = v / f with f fixed.decreases
- Frequency. The frequency stays the same, as it is set by the source.same
- Write the answer. Accept any answer that says the speed and wavelength decrease, and the frequency stays the same.
Check. ✓