Cairo University Problem set #1, 2024/2025
Faculty of Engineering Principles of acoustic & USW
Dept. of Eng. Math. & Phys. Aerospace & Aeronautic Engineering
1) The displacement function s(x,t) of a sound wave propagating in air (having an
equilibrium density = 1.2 kg/m3) is given by:
s(x, t) = 2 10−6 cos ( 40 x − 1.36*104 t ) m
(all values are in SI units)
Determine:
i- The wavelength and frequency of the described wave.
ii- The bulk modulus of the medium.
iii- The maximum speed of the molecules’ oscillatory motion.
iv- The maximum pressure variation caused by the sound wave.
v- The sound intensity.
vi- The sound intensity level in decibels.
vii- The instantaneous displacement of the medium molecules at the position
x = 34 cm at t = 10 s.
2) Repeat problem (1) if the maximum displacement is doubled while the frequency is
kept unchanged with zero initial phase. Comment on your results.
3) Repeat problem (1) if the frequency of the sound wave is doubled while the maximum
displacement is kept unchanged with zero initial phase. Comment on results.
4) The change in pressure (P) due to the propagation of a sound wave in a medium is given by:
P = 0.4 sin 4 (x − 340t ) in SI units
If the sound intensity level is 100 dbs, determine the maximum speed (in cm/s) of the
molecules’ oscillatory motion.
5) a- Show that the difference in decibel levels (1and 2) for two observers at distances
of r1 and r2 from a sound source is:
r
2 − 1 = 20 log 10 1
r2
b- A speaker is placed between two observers who are 110 m apart, along the line connecting
them. If one observer records an intensity level of 60 dB, and the other records an intensity level of
80 dB; how far is the speaker from each observer.
6) a- The output power of a certain stereo speaker is 6.0 watts. Determine the distance
from the speaker where: i- the sound is painful to the ear.
ii- the sound is barely audible.
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Cairo University Problem set #1, 2024/2025
Faculty of Engineering Principles of acoustic & USW
Dept. of Eng. Math. & Phys. Aerospace & Aeronautic Engineering
7) A white car is traveling at 72 km/h and emits a whistle at 320 Hz. A red car, initially
behind the white one, travels at 144 km/h and its horn sounds at 510 Hz. Determine the
sound frequencies observed by the drivers in the following cases:
i- The red car is behind the white one.
ii- The red car is in front of the white one. (The speed of sound in air is 340 m/s).
8) A train is traveling at a speed of 72 km/h and emits a sound at a frequency of 600 Hz.
A second train is coming towards the first one at a speed of 54 km/h. Determine the sound
frequency observed by a passenger in the second train in the following cases:
i- Before the meeting of the two trains.
ii- After the meeting of the two trains. (The speed of sound in air is 340 m/s).
Comment on the obtained results.
9) Repeat problem (8) if the two trains are moving with the same speed (72 km/h).
10) A car is moving towards a huge obstacle at a speed of 112 km/h and its horn sounds at
510 Hz. Determine the frequency of the echo heard by the driver. (The speed of sound in
air is 340 m/s).
11) A sound wave propagates in air at a speed 5.25
of 339 m/s. Air equilibrium density is 1.18
kg/m3. This causes the oscillations of air 3.50
particles about their equilibrium positions.
Particle speed (10-2 m/s)
The resulting time variation of particles speed 1.75
at a determined position is shown in figure.
0.00
Using data included in graph, determine:
i- The maximum displacement of the air -1.75
particles (in m).
ii- The maximum change in pressure. -3.50
iii- The maximum acceleration of the
molecules’ oscillatory motion. -5.25
iv- The sound intensity level in decibels. 0 50 100 150 200 250 300
v- The bulk modulus of the medium. time (s)
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