Name:
Grade 10 Physics
Module P3 Longitudinal waves and sound
Longitudinal waves
We have already looked at Transverse waves. In transverse waves the direction of disturbance is
perpendicular to the direction of propagation (or the direction in which the wave moves).
We will now consider longitudinal waves in which the disturbance is parallel (in the same direction) to the
direction of wave propagation. The best example of a longitudinal wave is a sound wave.
It is very easy to see the relationship between a transverse wave and its graphical representation
because they are essentially identical.
However, for longitudinal waves it is not as easy to see how a disturbance parallel to the direction of
propagation (e.g. a slinky) can in fact produce the same graph.
Starting position of all of the
particles
1
0
-2
-1
1
-2
1
1
0
+1 + 2
+2
1
0 -2
-1 - 1
2
0
+
1
2
Displacement position of all
of the particles
Compression
Rarefaction
1
Compression
1
1
Rarefaction
1
The position of the strands are 0, -2 , -1, -2, +0, +2 , +1, +2, 0 respectively; according to the number of places
which the strand have moved relative to its start position, if we now plot these displacements we can also
produce a sine graph to show the movement of a longitudinal wave.
1
+
𝟏
𝟐
Displacement
from equilibrium 0
position
𝟏
-𝟐
Distance from
source
-1
Grade 10 Module P3 Longitudinal waves
Page 1
Sound
Sound is created by the vibration of air particles. If you hold your hand directly in front of your mouth and you
talk, you can actually feel the air particles moving around and carrying the vibration. Your ear is able to
convert these vibrations into what you hear as sound. If you put your fingers on your neck while you are
speaking you can also feel your voice box (called the Larynx) making the vibrations that produce your voice.
When a boy’s voice “breaks” during puberty this is because the larynx grows larger and thicker causing the
sound produced to have deeper pitch, caused by a lower frequency.
Musical instruments also produce sounds by having strings or wind vibrate which produces a note.
The vibrations of sound create compressions and rarefactions in a sound wave. Sound waves the air particles
to move closer together in a compression and further apart in a rarefaction.
The wavelength of a sound wave is the distance between the center of two consecutive compressions.
Sound waves cannot move without a medium (solid, liquid or gas) to travel through.
This means that sound cannot travel through a vacuum. Outer space is an example of a vaccuum, as is a
container that has all of the gas (usually air) sucked out of it.
Interestingly enough if there was a huge explosion in outer space we would not hear it at all as there would
not be air particles to transmit the sound wave!
Sound waves can travel through a solid, liquid or gas. The closer the particles of matter are to each other the
faster the sound travels. This means that sound travels fastest through a solid, slower through a liquid and
slowest through a gas.
Grade 10 Module P3 Longitudinal waves
Page 2
The Pitch and Loudness of a sound
The frequency of a sound affects the pitch of the sound. High pitched and squeaky sounds have a higher
frequency than deep and lower pitched sounds.
The loudness of a sound is shown by the amplitude of the sound wave. Loud sounds have a large amplitude
and soft sounds have a smaller amplitude.
The frequency of a wave tells us how many vibrations occur in a time of one second. Frequency is measured
in Hertz (Hz)
Higher frequency
Lower frequency
The two waves shown above have the same amplitude and therefore are equally loud, but the wave on the
left hand side has a higher frequency and therefore a higher pitch.
The amplitude of a wave is the maximum movement of the particle in a vibration from their resting positions.
Larger amplitude
Smaller amplitude
The wave on the left has a larger amplitude and is therefore a louder sound than the wave on the right which
is a quieter sound due to its smaller amplitude.
Grade 10 Module P3 Longitudinal waves
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Musical instruments work by creating vibrations in the air particles which in turn create sound. The different
frequencies and amplitudes are perceived by our ears as different notes.
Ultrasound
Humans can hear waves with frequencies of between 20 Hz and 20 000 Hz, waves that have higher
frequencies are not audible to the human ear. We call these frequencies Ultrasonic. Bats use ultrasound to
locate insects and sense their environments. Ultrasonic waves are also used to form pictures of the different
tissues in human bodies, and is often used instead of an X-ray when and X – ray is considered high risk.
Echoes
When a sound wave reflects off a solid surface it can create an echo. Echoes can only be distinguished if
there is more than a 0,1 second delay between the original sound and its reflection, otherwise your ears only
detect one sound.
Echoes can cause disturbance and “noise” in rooms which have poor acoustics, hall’s and concert venues
often have soft furnishings to absorb the echoes.
Echoes have useful applications as well such as Sonar, which can detect the presence of underwater objects,
and in geophysical prospecting which allows us to determine the presence of mineral and oil reserves under
the surface of the earth.
Grade 10 Module P3 Longitudinal waves
Page 4
Grade 10 Physics
Module P3 Worksheet Longitudinal waves and
sound
QUESTION 1
1.1
Which of the following media can a longitudinal wave like sound NOT travel through?
A
B
C
D
1.2
solid
liquid
gas
vacuum
(2)
The diagrams below show three sound wave sketches as depicted on the screen of an oscilloscope.
Each block on the graph represents one unit.
Which one of the following statements is CORRECT?
A
B
C
D
1.3
Wave 1 and wave 3 have the same frequency.
Wave 2 and wave 3 have the same loudness.
Wave 1 and wave 2 have the same pitch.
Wave 2 is a softer sound than wave 1.
(2)
Two points, labelled X and Y, are shown on the wave below.
X
Y
The number of wavelengths equal to the horizontal distance between points X and Y is:
A
1½
B
2
C
2½
D
3
Grade 10 Module P3 Longitudinal waves
Page 5
(2)
1.4
A tuning fork, a violin string and a loudspeaker are producing sounds. This is because they are all in a
state of:
A
compression
B
rarefaction
C
tension
D
vibration
(2)
1.5
If a note played on a piano has the same pitch as one played on a guitar, the two notes will have the
same:
A
B
C
D
1.6
(2)
Explosions do not occur in space.
Sound cannot travel through a vacuum.
Sound is reflected away from the spaceship.
Sound travels too quickly in space to affect the ear drum.
(2)
A sound wave is different from a light wave in that a sound wave is:
A
B
C
D
1.9
2 Hz → 2 000 Hz
20 Hz → 20 000 Hz
200 Hz → 200 000 Hz
2 000 Hz → 2 000 000 Hz
Astronauts are in a spaceship orbiting the moon. They see an explosion on the surface of the moon.
Why can they not hear the explosion?
A
B
C
D
1.8
(2)
What is the approximate range of audible frequencies for a healthy human?
A
B
C
D
1.7
Amplitude
Loudness
Quality
Frequency
produced by a vibrating object and a light wave is not.
not capable of travelling through a vacuum.
not capable of diffracting and a light wave is.
capable of existing with a variety of frequencies and a light wave has a single frequency.
(2)
At the same temperature, sound waves have the fastest speed in:
A
B
C
D
rock
milk
oxygen
sand
Grade 10 Module P3 Longitudinal waves
(2)
Page 6
1.10 Two sound waves are travelling through a container of nitrogen gas. The first wave has a wavelength
of 1,5 m, while the second wave has a wavelength of 4,5 m. The velocity of the second wave must
be:
A
B
C
D
1/3 the velocity of the first wave
the same as the velocity of the first wave
three times larger than the velocity of the first wave
nine times larger than the velocity of the first wave
(2)
1.11 If the velocity of the wave remains constant, which one of the following increases when the
wavelength decreases
A
B
C
D
Frequency
Amplitude
Speed
Period
(2)
1.12 The time required for a wave to complete ONE full cycle is called the:
A
B
C
D
frequency
wavelength
speed
period
[24]
QUESTION 2
The following longitudinal wave has a distance of 2 m between points X and Y. It takes 0,5 s for a particle
of the medium to make one complete vibration.
2.1
2.2
2.3
2.4
2.5
2.6
Define a longitudinal wave.
What do the letters A and B represent?
What is the wavelength of the wave?
Calculate the frequency of the wave.
Calculate the speed of the wave.
Give an example of energy that moves as longitudinal waves.
Grade 10 Module P3 Longitudinal waves
(2)
(2)
(2)
(3)
(3)
(1)
[13]
Page 7
QUESTION 3
cliff 2
cliff 1
A man stands between two cliffs as shown in the
diagram. He claps his hands once. The distances
away from each cliff is given below.
165 m
110 m
Take the speed of sound to be 330 ms-1 on that
day. Calculate the time interval between the two
loudest echoes that he hears.
[7]
QUESTION 4
4.1
A dolphin emits an ultrasonic wave with frequency of 0,15 MHz. The speed of the ultrasonic wave in
water is 1500 m·s−1. What is the wavelength of this wave in water?
(3)
4.2
Humans can detect frequencies as high as 20 000 Hz. Assuming the speed of sound in air is 344
m·s−1, calculate the wavelength of the sound corresponding to the upper range of audible hearing. (3)
4.3
An elephant trumpets at 10 Hz. Assuming the speed of sound in air is 344 m·s−1 , calculate the
wavelength of this infrasonic sound wave made by the elephant.
(3)
4.4
A ship sends a signal out to determine the depth of the ocean. The signal returns 2,5 seconds later. If
sound travels at 1450 m·s−1 in sea water, how deep is the ocean at that point?
(4)
4.5
A person shouts at a cliff and hears an echo from the cliff 1 s later. If the speed of sound is 344 m·s −1,
how far away is the cliff?
(4)
[17]
QUESTION 5
A learner decides to do an investigation on the speed of sound. The learner holds a drum 10 m from a wall,
a sound detector which he placed before taking up his position is a distance behind him.
When the learner hits the drum ONCE, the sound detector detects TWO sounds. Take the speed of sound
in air is 330 m·s-1.
10m
5.1
Explain why the detector records two sounds.
(2)
5.2
The second sound reached the detector 0,15s after the learner hit the drum. Calculate the distance
between the learner and the sound detector.
(4)
5.3
What would the result have been it the experiment was done in a vacuum? Give a reason for the
answer.
(2)
[8]
Grade 10 Module P3 Longitudinal waves
Page 8
QUESTION 6
The graph below, not drawn to scale, represents two sound waves, A and B, of the same wavelength but
different amplitudes, crossing each other for a time of 0,15s.
0,15s
6.1
Are the waves TRANSVERSE or LONGITUDINAL waves?
(1)
6.2
State the principle of superposition of waves.
(2)
6.3
The amplitude of wave B is two thirds (3) the amplitude of wave A. Calculate the amplitude of
2
wave B.
(2)
6.4
Draw the shape of the resulting wave form as the two waves meet onto the image above.
(3)
6.5
What type of interference has occurred. Answer only CONSTRUCTIVE or DESTRUCTIVE.
6.6
Will the resulting sound be lounder or softer than before?
6.7
Wave A travels a distance of 0,6m in a time of 0,15s. Calculate the:
(1)
(1)
6.7.1
Speed of wave A.
(3)
6.7.2
frequency of wave A.
(2)
Grade 10 Module P3 Longitudinal waves
Page 9
QUESTION 7
Experiments were done to investigate the effect of temperature on the speed of sound. One person beat a
drum while another person, who was standing 50 m away from the sound source, recorded the time
travelled by the sound.
They performed the experiment at different temperatures at different times of the day. They recorded their
findings in the table below.
Temperature (°C)
0
5
10
15
20
25
7.1
Time (s)
0,151
0,150
0,148
0,147
0,146
0,145
For the investigation, write down the:
7.1.1
7.1.2
7.1.3
Investigative question
Independent variable
Dependent variable
(2)
(1)
(1)
7.2
Calculate the speed of sound in air at 20°C.
(3)
7.3
Write down the conclusion for the investigation.
(2)
The person who beat the drum, noticed that the sound reflected back after a while.
7.4
Name the term used to describe the reflection of the sound waves.
(1)
[10]
Grade 10 Physics
Longitudinal wave:
Compression:
Rarefaction:
Wavelength:
Module P3 Definitions
Longitudinal waves
A wave in which the particles of the medium vibrate in the direction of
propagation of the wave.
The region in a longitudinal wave where the particles are closest together.
The region in a transverse wave where the particles are further apart.
The distance between the centres of two consecutive compressions.
Grade 10 Module P3 Longitudinal waves
Page 10