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9 Common Problems of Sound Waves Learning sound waves in 9 common problems with the solutions, sound intensity, sound intensity level, doppler effect and fundamental frequency of sound sources will be discussed.

Problem 1

Find the intensity level of a sound wave of 10-5 watt/m2 in intensity . Use a reference intensity I0 = 10-12 watt/m2!

The formula to calculate a sound level intensity is

so then

Problem 2

A boy stands at 100 m of distance from a sound source with its acoustic power of 12,56 watt. Find the sound intensity level heard by this boy, use Π = 3,14 with a reference intensity of I0 = 10-12 watt/m2!

Equation to find the sound intesity level is

Where TI is the sound intensity level, and intensity level or I is

with P = the acoustic power in watt and A = area in m2, assume the acoustic power spread uniformly so then we get the area of a sphere, A = 4Πr2, with r is sphere radius or the distance between the boy and the point taken.


Problem 3
A boy heard a loud bang of 120 dB in sound intensity level at a distance of 20 m .

Find the soun intensity level heard by another boy at distance of 180 m from the first boy!

The sound intensity level of two different distances:

with r1 the first distance to the source (20 m) and r2 is the second distance from the source (180+20 = 200 m) so then we get

Problem 4
A factory has 100 identical machines. If the sound intensity level of a machine is 70 dB, find the 100 machines sound intensity level!


Finding the sound intensity level of n identical sources:

where TI1 sound intensity level of a source and n is the number of sources, so then

Problem 5
Find the ratio of intensities from two sources at two different distances that are 4m and 9 m from the sound source!

Intensities from two different distances are:

Problem 6
A boy hears two different sounds when a race car is moving toward and moving away. If the speed of sound in the air is 340 m.s-1 , the frequency emitted by the car is 800 Hz and the car velocity is l 20 m.s-1, find the frequency heard by the boy when the car moving toward!

Its the doppler effect of sound waves, where the speed of listener Vp = NOL, the boy at rest, the sign for Vs is negative, the source moving towrd, so then

Problem 7
A source emits a frequency of 1 kHz is moving toward a rest listener with a speed of 0,9v, where v is the speed of sound wave. Find the frequency heard by the listener!

Doppler effect, the listener at rest:

Problem 8

Given a string of 0,5 m of length and 10−2 kg of mass with its tension of 200 N. Find the fundamental frequency of the string!

Sound wave speed along a string :

The fundamental frequency of a string happens when the length of string:

String frequency:

The shorcut for this question is :

Problem 9
A stopped pipe emits a fundamental frequency of 150 Hz. Find the second harmonic of this pipe!

The ratio of frequencies of the fundamental, the second harmonic, the third harmonic of a stopped pipe are:

So then :

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