__Summary of Chapter 18__

**1. **** Sound waves are
longitudinal**; that is the particles of the medium move parallel to the direction of
motion of the wave.

The
velocity of sound in different media is given by;

_{} where Y is the Young
modulus _{}

_{} where B is the Bulk
modulus _{}

v_{air}
= 343 m/s at a temperature of about 20 ^{o}C and v_{vacuum} = 0

**2. **A harmonic sound wave can be
described by a * displacement wave*
or a

* *

** The
displacement wave** for a harmonic sound wave is given by;

_{}

where s(x,t) is the
diplacement of the particles in the medium, *k* is the wave

number, *w* is the angular frequency,
and *S _{m}* is the displacement amplitude.

* *

** The
pressure wave** is given by;

_{}

Where

_{}

*D**P _{m} *is the pressure amplitude
and

**3. **__Interference of sound waves____ __

The relationship between the difference in path and
the phase difference between the two sound waves at the location of a listener
is

_{}

*D**L* is the path length difference between the two sound
waves.

**2 Cases:**

*a)
***Constructive interference** (maximum sound) *D**L = 0,
**l**, 2**l**, 3**l** *

Þ _{} for n = 0, 1, 2, 3, 4,

b)
**Destructive interference** (minimum sound) Dr = 0, l/2, l, 3l/2 .

Þ _{} for n = 1, 3, 5, 7,

**4. **** The power** transmitted in a harmonic
sound wave is given by;

_{}

** The intensity** of a sound wave I is
defined as

Þ _{}

Since the intensity of sound varies between
10^{-12} W/m^{2} to 1 W/m^{2} we define a new quantity
called ** sound intensity level** b as

_{}

where I_{o} = 10^{-12} W.m^{2} is the reference
intensity.

The units for b is dB (Decibel). Now b varies between 0 and 120 dB.

For ** spherical sound waves**, the intensity is
given by;

_{}

(r: distance between the source and the point
where we want to measure the intensity).

_{} and _{} Þ
_{}

**Standing Waves in air columns (pipes)**

Sound sources can be used to produce longitudinal standing waves in air columns.

2 Cases:

a)
** pipe
open at both ends**: The resonances occur for

L = n l/2 for
n = 1, 2, 3, 4, ..

since v = lf Þ ** **
**f = (n v)/2L ** for n = 1, 2, 3, 4, ..

where v is the speed of sound waves

b)
** pipe
closed at one end**: the resonances occur when

L = n l/4 for n = 1, 3, 5, 7,

Þ ** ** **f = n v/4L**
for
n = 1, 3, 5, 7,

** **

**6.
**The Doppler Effect

The Doppler effect
is the change in frequency *f* heard by a detector whenever there is relative motion between a source and a
detector. There are 8 cases described as follows:

Detector Source Equation

D S _{}Detector moving toward
stationary source

D S _{}Detector moving away
from stationary source

D S _{}Source moving away from
a stationary detector

D S _{}
Source moving toward a stationary
detector

D S _{}Detector approaching
and source is moving away

D S _{}Source approaching and
detector moving away

D S _{}Source and detector are
both approaching

D S _{} Source and detector
are both moving away

**InGeneral **_{}