Sound
Sound waves are longitudinal: they have compressions and rarefactions and oscillate backwards
and forwards.
Humans can hear frequencies between 20 and 20 000Hz.
Sound waves need a medium (a material) to travel through
Compression: high pressure section of the wave
Rarefaction: low pressure section of the wave
Speed of sound is highest in solids (concrete: 5000m/s) then in liquids (pure water: 1400m/s) and
slowest in gases (air: 330m/s)
Measurement of the speed of sound
Echo method
An estimate of the speed of sound in air can be made directly if you stand about 100 metres from
a high wall or building and clap your hands. Echoes are produced. When the clapping rate is such
that each clap coincides with the echo of the previous one, the sound has travelled to the wall and
back in the time between two claps, i.e. one interval. By timing 30 intervals with a stopwatch, the
time t for one interval can be found. Also, knowing the distance d to the wall, a rough value is
obtained from
2𝑑
𝑠𝑝𝑒𝑒𝑑 𝑜𝑓 𝑠𝑜𝑢𝑛𝑑 𝑖𝑛 𝑎𝑖𝑟 =
𝑡
Example 1
a) A girl stands 160m away from a high wall and claps her hands at a steady rate so that each clap
coincides with the echo of the one before. If her clapping rate is 60 per minute, state the value
this gives for the speed of sound.
Solution
60 claps = 1min = 60s
1 interval = 1s (which is equals to time taken by the sound to the high wall and back)
2𝑑
𝑠𝑝𝑒𝑒𝑑 𝑜𝑓 𝑠𝑜𝑢𝑛𝑑 𝑖𝑛 𝑎𝑖𝑟 =
𝑡
2𝑥160𝑚
𝑠𝑝𝑒𝑒𝑑 𝑜𝑓 𝑠𝑜𝑢𝑛𝑑 𝑖𝑛 𝑎𝑖𝑟 =
1𝑠
𝑠𝑝𝑒𝑒𝑑 𝑜𝑓 𝑠𝑜𝑢𝑛𝑑 𝑖𝑛 𝑎𝑖𝑟 = 320𝑚/𝑠
b) If she moves 40m closer to the wall she finds the clapping rate has to be 80 per minute. Calculate
the value these measurements give for the speed of sound.
Solution
80 claps = 1min = 60s
1 interval = 60/80s = 0.75s (which is equals to time taken by the sound to the high wall and
back)
d = 120m (she moves 40m closer to the wall)
2𝑑
𝑠𝑝𝑒𝑒𝑑 𝑜𝑓 𝑠𝑜𝑢𝑛𝑑 𝑖𝑛 𝑎𝑖𝑟 =
𝑡
2𝑥120𝑚
𝑠𝑝𝑒𝑒𝑑 𝑜𝑓 𝑠𝑜𝑢𝑛𝑑 𝑖𝑛 𝑎𝑖𝑟 =
0.75𝑠
𝑠𝑝𝑒𝑒𝑑 𝑜𝑓 𝑠𝑜𝑢𝑛𝑑 𝑖𝑛 𝑎𝑖𝑟 = 320𝑚/𝑠
Exercise
c) She moves again and finds the clapping rate becomes 30 per minute. Calculate how far she is
from the wall if the wave speed of sound is the value you found in (a).
Direct method
The speed of sound in air can be found directly by measuring the time t taken for a sound to travel
past two microphones separated by a distance d:
𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑡𝑟𝑎𝑣𝑒𝑙𝑙𝑒𝑑 𝑏𝑦 𝑡ℎ𝑒 𝑠𝑜𝑢𝑛𝑑
𝑠𝑝𝑒𝑒𝑑 𝑜𝑓 𝑠𝑜𝑢𝑛𝑑 𝑖𝑛 𝑎𝑖𝑟 =
𝑡𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛
𝑑
=
𝑡
This method can also be used to find the speed of sound in different materials. For example, placing
a metal bar between the microphones would allow the speed of sound in the metal to be determined.
Musical notes
Regular vibrations by musical instruments produce musical notes, which have three properties –
pitch, loudness and quality.
Pitch- The pitch of a note depends on the frequency of the sound wave reaching the ear
Higher frequency → a higher pitch
Loudness- The loudness of a note depends on the amplitude of the sound wave reaching the ear
Larger amplitude → louder sound (the more sound enters your ear the louder it becomes).
Exercise
1. a) Explain with reference to a sound wave what is meant by the terms
i) Compression
ii) Rarefaction
b) State how far a compression and the nearest rarefaction are apart in terms of the wavelength
of a sound wave
c) A sound wave has a frequency of 220Hz and travels in air with a speed of 330m/s. Calculate
the distance between consecutive rarefactions
2. A fishing vessel is using sonar to monitor the position of shoals of fish. Calculate the depth of
a shoal if an ultrasound pulse reflected from the shoal takes 0.5 s to return to the ship. Take the
speed of sound in water to be 1400 m/s.
3 A student plays the violin near the doorway to a large room. Fig. 3.1 shows a young teacher
standing where he can hear the sound but cannot see the student.
Fig. 3.1
a) State the wave effect that allows the young teacher to hear sounds from the violin at the
position he is standing in Fig. 3.1.
................................................................................................................................... [1]
b) Calculate the frequency of sound with a wavelength of 0.75m.
The speed of sound in air is 340m/s.
frequency = ......................................................... [2]
c) A violin produces sounds in the frequency range 200Hz–3800Hz.
The width of the open doorway is 0.75m.
Explain why the young teacher hears the frequency calculated in (a)(ii) clearly but finds a
frequency of 3500Hz much harder to hear.
...........................................................................................................................................
...........................................................................................................................................
..................................................................................................................................... [2]
4 (a) A sound wave travels through air. Fig. 4.1 shows a pressure–time graph for the air at one
place
Fig. 4.1
(i) On Fig. 4.1:
• label one point C to indicate a compression
• label one point R to indicate a rarefaction. [2]
(ii) Explain why this graph cannot be used to find the wavelength of the sound wave.
...........................................................................................................................................
….................................................................................................................................. [1]
(iii) The sound becomes louder and of lower pitch.
State what happens to:
the amplitude of the sound
...........................................................................................................................................
the frequency of the sound.
........................................................................................................................................... [1]
(b) A sound of frequency 13kHz is transmitted through water.
The speed of sound in water is 1500m/s.
Calculate the wavelength of this sound in water.
wavelength = ......................................................... [3]
(c) State the approximate speed of sound in air.
speed = ......................................................... [1]
