## 9 Common Problems of Sound Waves

- Category: High School
- Written by fisikastudycenter

physics.fisikastudycenter.com- 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/m^{2} in intensity . Use a reference
intensity I_{0} = 10^{-12} watt/m^{2}!

**Answer**

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 I_{0} = 10^{-12}
watt/m^{2}!

**Answer**

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 m^{2}, assume the acoustic power spread uniformly so then
we get the area of a sphere, A = 4Πr^{2}, with r is sphere radius or the distance between the boy and the
point taken.

then:

**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!

**Answer**

The sound intensity level of two different distances:

with
r_{1} the first distance to the source (20 m) and r_{2} 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!

**Answer**

Finding the sound intensity level of n identical sources:

where TI_{1} 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!**Answer**

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!**Answer**

Its the doppler effect of sound
waves, where the speed of listener V_{p} = NOL, the boy at rest, the sign for V_{s} 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 0,9*v*, where
*v* is the speed of sound wave. Find the frequency heard by the listener!

**Answer**

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!**Answer**

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!**Answer**

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

So then
: