Waves and sound
Waves and Sound
Edited by: MGROSALES
There are mainly 2 types of waves:
Mechanical waves-somephysical medium is
being disturbed
em waves- do not require a medium to
propagate
Mechanical waves:
Water waves- without water, there would be
no wave. A wave traveling on a string would
not exist
The Nature of Waves
1. A wave is a traveling disturbance.
2. A wave carries energy from place to place.
Transverse Waves
• A traveling wave or pulse that causes the
elements of the disturbed medium to move
perpendicular to the direction of propagation is
called Transverse waves.
• a transverse wave is one in which the
disturbance occurs perpendicular to the
direction of travel of the wave. Radio waves,
light waves, and microwaves are transverse
waves. Transverse waves also travel on the
strings of instruments such as guitars and
banjos.
Longitudinal waves
• A traveling wave or pulse that causes the
elements of the medium to move parallel
to the direction to the direction of
propagation is called longitudinal waves.
The Nature of Waves
Transverse Wave
The Nature of Waves
Longitudinal Wave
The Nature of Waves
Water waves are partially transverse and partially longitudinal.
Periodic Waves
Periodic waves consist of cycles or patterns that are produced over and
over again by the source.
In the figures, every segment of the slinky vibrates in simple harmonic
motion, provided the end of the slinky is moved in simple harmonic
motion.
Periodic Waves
In the drawing, one cycle is shaded in color.
The amplitude A is the maximum excursion of a particle of the medium from
the particles undisturbed position.
The wavelength is the horizontal length of one cycle of the wave.
The period is the time required for one complete cycle.
The frequency is related to the period and has units of Hz, or s-1.
1
f =
T
Periodic Waves
v=

T
= f
Periodic Waves
Example 1 The Wavelengths of Radio Waves
AM and FM radio waves are transverse waves consisting of electric and
magnetic field disturbances traveling at a speed of 3.00x108m/s. A station
broadcasts AM radio waves whose frequency is 1230x103Hz and an FM
radio wave whose frequency is 91.9x106Hz. Find the distance between
adjacent crests in each wave.
v=

T
= f
v
=
f
Periodic Waves
AM
FM
v 3.00 108 m s
= =
= 244 m
3
f 1230 10 Hz
v 3.00 108 m s
= =
= 3.26 m
6
f
91.9 10 Hz
The Speed of a Wave on a String
The speed at which the wave moves to the right depends on how quickly
one particle of the string is accelerated upward in response to the net
pulling force.
tension
F
v=
mL
linear density
The Speed of a Wave on a String
Example 2 Waves Traveling on Guitar Strings
Transverse waves travel on each string of an electric guitar after the
string is plucked. The length of each string between its two fixed ends
is 0.628 m, and the mass is 0.208 g for the highest pitched E string and
3.32 g for the lowest pitched E string. Each string is under a tension
of 226 N. Find the speeds of the waves on the two strings.
The Speed of a Wave on a String
High E
v=
F
=
mL
226 N
= 826 m s
-3
0.208 10 kg (0.628 m )
(
)
Low E
v=
F
=
mL
226 N
= 207 m s
-3
3.32 10 kg (0.628 m )
(
)
The Mathematical Description of a Wave
What is the displacement y at time t of a
particle located at x?
The Nature of Sound Waves
LONGITUDINAL SOUND WAVES
Sound
• A longitudinal wave that is created by a
vibrating object ( guitar, vocal chords,
diaphragms of speaker.
• Sound can can be created or transmitted
only in a medium (gas, liquid or gas
The Nature of Sound Waves
The distance between adjacent condensations is equal to the
wavelength of the sound wave.
The Nature of Sound Waves
Individual air molecules are not carried along with the wave.
The Nature of Sound Waves
THE FREQUENCY OF A SOUND WAVE
The frequency is the number of cycles
per second.
A sound with a single frequency is called
a pure tone.
The brain interprets the frequency in terms
of the subjective quality called pitch.
The Nature of Sound Waves
THE PRESSURE AMPLITUDE OF A SOUND WAVE
Loudness is an attribute of
a sound that depends primarily
on the pressure amplitude
of the wave.
The Speed of Sound
Sound travels through gases,
liquids, and solids at considerably
different speeds.
The Speed of Sound
In a gas, it is only when molecules collide that the condensations and
rarefactions of a sound wave can move from place to place.
vrms =
Ideal Gas
v=
 kT
3kT
m
k = 1.38 10 −23 J K
m
5
7
 = for monatomic or diatomic
3
5

= Cp/Cv
Specific heat ratio = the ratio of the specific
heat capacity at constant pressure cp to
the specific
heat capacity at constant volume cv.
The Speed of Sound
LIQUIDS
v=
Bad

SOLID BARS
v=
Y

Sound Intensity
Sound waves carry energy that can be used to do work.
The amount of energy transported per second is called the
power of the wave.
The sound intensity is defined as the power that passes perpendicularly
through a surface divided by the area of that surface.
P
I=
A
Sound Intensity
Example 6 Sound Intensities
12x10-5W of sound power passed through the surfaces labeled 1 and 2. The
areas of these surfaces are 4.0m2 and 12m2. Determine the sound intensity
at each surface.
Sound Intensity
P 12 10−5 W
−5
2
I1 =
=
=
3
.
0

10
W
m
A1
4.0m2
P 12 10−5 W
−5
2
I2 =
=
=
1
.
0

10
W
m
A2
12m2
Sound Intensity
For a 1000 Hz tone, the smallest sound intensity that the human ear
can detect is about 1x10-12W/m2. This intensity is called the threshold
of hearing.
On the other extreme, continuous exposure to intensities greater than
1W/m2 can be painful.
If the source emits sound uniformly in all directions, the intensity depends
on the distance from the source in a simple way.
Sound Intensity
power of sound source
P
I=
4 r 2
area of sphere
Decibels
The decibel (dB) is a measurement unit used when comparing two sound
intensities.
Because of the way in which the human hearing mechanism responds to
intensity, it is appropriate to use a logarithmic scale called the intensity
level:
I 
 = (10 dB) log 
 Io 
I o = 1.00  10 −12 W m 2
Note that log(1)=0, so when the intensity
of the sound is equal to the threshold of
hearing, the intensity level is zero.
Decibels
I 
 = (10 dB) log 
 Io 
I o = 1.00  10 −12 W m 2
Decibels
Example 9 Comparing Sound Intensities
Audio system 1 produces a sound intensity level of 90.0 dB, and system
2 produces an intensity level of 93.0 dB. Determine the ratio of intensities.
I 
 = (10 dB) log 
 Io 
Decibels
I 

I
 o
 = (10 dB) log
I 
 Io 
I 
 Io 
1 = (10 dB) log 1 
 2 = (10 dB) log 2 
I 
 Io 
I 
 Io 
 I Io 
I 
 = (10 dB) log 2 
 I1 
 I1 I o 
 2 − 1 = (10 dB) log 2  − (10 dB) log 1  = (10 dB) log 2
 I2 
3.0 dB = (10 dB) log 
 I1 
 I2 
0.30 = log 
 I1 
I2
= 100.30 = 2.0
I1
Doppler Effect
• A change in frequency or pitch of the
sound detected by an observer because
the sound source and the observer have
different velocities with respect to the
medium of sound propagation.
Moving source
• Numerator, (+) – O moves toward source
• (-) O moves away from source
• Denominator, (-) source moves toward the O
• (+) source moves away from O
16.8 The Doppler Effect
The Doppler Effect II—moving listener, moving source
❑ As the object making the sound moves or as the listener moves
(or as they both move), the velocity of sound is shifted enough to
change the pitch perceptively.
Example 16.15 Doppler effect I: Wavelengths
•
A police siren emits a sinusoidal wave with frequency fs = 300 Hz. The
speed of sound is 340 m/s. (a) Find the wavelength of the waves if the
siren is at rest in the air. (b) If the siren is moving at 30 m/s (108 km/h,
or 67 mi/h), find the wavelengths of the waves in front of and behind the
source.
Example 16.16 Doppler effect II: Frequencies
•
If a listener L is at rest and the siren in Example 16.15 is moving away
front L at 30 m/s, what frequency does the listener hear?
Example 16.17 Doppler effect III: A moving listener
•
If the siren is at rest and the listener is moving away front the siren at 30
m/s, what frequency does the listener hear?
Example 16.18 Doppler effect IV: Moving source, moving listener
•
If the siren is moving away front the listener with a speed of 45 m/s
relative to the air and the listener is moving toward the siren with a
speed of 15 m/s relative to the air, what frequency does the listener
hear?
Example 16.19 Doppler effect V: A double Doppler shift
•
The police car with its 300-Hz siren is moving toward a warehouse at 30
m/s, intending to crash through the door. What frequency does the
driver of the police car hear reflected front the warehouse?
❑ The frequency of sound reaching the warehouse, which we call fw , is
greater than 300 Hz because the source is approaching.
❑ In the second shift, the warehouse acts as a source of sound with
frequency fw , and the listener is the driver of the police car; she hears a
frequency greater than fw because she is approaching the source.
❑ To determine fw , we use Eq. (16.29) with fs replaced by fw . For this
part of the problem, vL = vw = 0 (the warehouse is at rest) and vs = -30
m/s (the siren is moving in the negative direction from source to
listener).
Doppler Effect for
Electromagnetic Waves
❑
❑
❑
❑
special relativity
c = speed of light
v = speed of source
fR = frequency at receiver
*16.9 Shock Waves
16.35 Wave crests around a sound source S moving (a) slightly
slower than the speed of sound v and (b) faster than the sound
speed v
(a) Source is slower than sound
(b) Supersonic source: faster than sound
Mach number = vs /v
sin = v/vs = 1/Mach no
•
(c) This photograph shows a T-38 jet airplane moving at 1.1 times the
speed of sound. Separate shock waves are produced by the nose,
wings, and tail. The angles of these waves vary because the air speeds
up and slows down as it moves around the airplane, so the relative
speed vs of the airplane and air is different for shock waves produced at
different points.
Example 16.20 Sonic boom from a supersonic airplane
•
An airplane is flying at Mach 1.75 at an altitude of 8000 m, where the
speed of sound is 320 m/s. How long after the plane passes directly
overhead will you hear the sonic boom?