CHAPTER 13 - SOUND
Objectives
13.1 – SOUND WAVES
* Explain how sound waves are produced
* Relate frequency to pitch
* Compare the speed of sound in various media
* Relate plane waves to spherical waves
* Recognize the Doppler effect, and determine the direction
of a frequency shift when there is relative motion between a
source and an observer.
WHERE SOUND WAVES COME FROM
Sound starts with a vibrating object
•
•
•
When an object vibrates, it sets the air molecules near it in motion
As a vibrating object moves to the right, the molecules on the right forced
closer together. This becomes a region of higher molecular density and
pressure. This is an area of compression.
As the vibrating object moves to the left, the molecules in the region to
the right now spread father apart, causing lower molecular density and
pressure. This is an area of rarefaction.
SOUND WAVES ARE LONGITUDINAL
What is the definition of a longitudinal wave?
A wave in which the direction of the vibrating particles
are parallel to the direction of wave travel
Longitudinal Waves and Particle Motion
FREQUENCY AND PITCH
Review: What is frequency?
Frequency is the number of cycles (or vibrations or oscillations, etc.)
per unit time. The units for cycles per second, or Hertz (Hz).
Audible sound waves for the average human are between
20 and 20,000 Hz.
Infrasonic sound waves are those with frequencies below 20 Hz
Ultrasonic sound waves are those with frequencies above 20,000 Hz
FREQUENCY AND PITCH, CONT.
Pitch is how high or low we perceive a sound wave to be.
The higher the frequency of a sound wave, the higher pitch
we perceive it to be.
Frequency is an objective, measureable quantity,
while pitch is simply a perception….
SOUND WAVES AND IMAGES
Sound waves with very short
wavelengths (i.e., ultrasonic
waves) can be used to create
visible images. Sound waves are
partially reflected when they
reach a boundary between
materials of two different
densities. Ultrasonic waves, with
their very short wavelengths, are
easily reflected off small objects.
SOUND WAVES AND IMAGES
Another example of using sound
waves to form images is called
echolocation (or sonar). Dolphins
and bats can send out high
frequency sound wave pulses that
are reflected back. The reflected
waves allow the dolphin or bat or
to form an image of the object
that caused the wave reflection.
SPEED OF SOUND
The speed of sound depends on the medium it is traveling through.
Sound can travel through solids, liquids or gases. Because
sounds waves travel via particle vibration, the speed of
sound depends on how fast a medium can transfer its
motion from one particle to another.
So, which medium would you expect sound to travel
through faster….a solid or a gas?
SPEED OF SOUND, CONT.
The speed of sound also is dependent on the temperature
of the medium, especially for gases. As air gets warmer, the
air molecules move around more and collide more frequently.
Therefore, sound vibrations moving from particle to particle
can happen faster in warmer air.
V = 331 + 0.6(T)
v is in m/s and T is in oC
For liquids and solids, temperature does not make much of a
difference because the molecules are so close together anyway.
HOW SOUND WAVES TRAVEL
We’ve seen pictures and animations of
longitudinal waves, and they all appear
to be one-dimensional. But sound waves
propagate in 3 dimensions.
The areas of compression are called
wavefronts. The distance between
consecutive wavefronts is a wavelength.
The direction of wave travel is spherically
outward (shown by red arrows).
THE DOPPLER EFFECT
The pitch of the car horn
gets higher as the car
gets closer to us, and gets
lower as the car gets
farther away….
But pitch is related to
frequency, and the
frequency of the car horn
isn’t changing, so how
does this work?
THE DOPPLER EFFECT, CONT.
Remember, pitch is the “perception”
of frequency. The relative motion of
the car makes this perception change.
As the car approaches you, the
wavefronts from the horn reach you
more frequently because the source of
the sound is moving toward you. As
the source of the sound moves away
from you, you perceive the pitch to be
lower because the wavefronts don’t
reach you as frequently.
DOPPLER EFFECT EQUATION
𝒗 ∓ 𝒗𝒐
fo = fs (
)
𝒗 ∓ 𝒗𝒔
fo = frequency the observer hears
vo = velocity of observer
vs = velocity of source
fs = normal frequency of the source sound (in air)
v = normal speed of sound in air (343 m/s)
USING THE DOPPLER EQUATION
If the OBSERVER is stationary:
• Then vo = 0
𝒗 ∓ 𝒗𝒐
fo = fs (
)
𝒗 ∓ 𝒗𝒔
•
•
•
fo decreases as source goes away from observer.
For fo to decrease, the denominator on the right side has to increase.
To increase denominator, use (v + vs).
•
•
•
fo increases as source gets closer to observer.
For fo to increase, the denominator on the right side has to decrease.
To decrease denominator, use (v - vs).
USING THE DOPPLER EQUATION, CONT.
If the SOURCE is stationary:
• Then vs = 0
𝒗 ∓ 𝒗𝒐
fo = fs (
)
𝒗 ∓ 𝒗𝒔
•
•
•
fo decreases as observer goes away from the source.
For fo to decrease, the numerator on the right side has to decrease.
To decrease numerator, use (v - vo).
•
•
•
fo increases as observer gets closer to the source.
For fo to increase, the numerator on the right side has to increase.
To increase numerator, use (v + vo).
DOPPLER EFFECT EXAMPLE PROBLEM
A train with horn blaring passes a station going 50 m/s.
If the people standing on the platform at the station
hear the frequency as 384 Hz after the train passes,
what is the frequency of the train horn?
Ans: 440 Hz
𝒗 ∓ 𝒗𝒐
fo = f s (
)
𝒗 ∓ 𝒗𝒔
13.2 – SOUND INTENSITY AND RESONANCE
Objectives
* Calculate the intensity of sound waves
* Relate intensity, decibel level, and perceived loudness
* Explain why resonance occurs
SOUND INTENSITY
Intensity is the rate of energy flow through a unit area
perpendicular to the direction of wave motion.
Intensity =
Δ𝐸
Δ𝑡
𝐴𝑟𝑒𝑎
Because power, P, is defined as the rate of energy transfer,
we can also describe intensity in terms of power.
𝑃
Intensity =
𝐴𝑟𝑒𝑎
SOUND INTENSITY, CONT.
Intensity
𝑃
=
𝐴𝑟𝑒𝑎
Units for power are?
Units for area are?
So, units for intensity are?
Since sound propagates outward in all directions equally, the
area affected by the intensity is the surface area of a sphere (4r2).
Intensity =
𝑷
𝟒𝒓𝟐
Where r is the distance
from the sound source
SOUND INTENSITY, CONT.
So, the farther you get
away from the source of
a sound, the less intense
the sound because the
energy of the sound is
spread out over a larger
area.
SOUND INTENSITY, EXAMPLE
What is the intensity of sound waves produced by a
trumpet at a distance of 3.2m if the power output of
the trumpet is 0.20W? Assume the sound waves are
spherical.
Ans: 1.6 x 10-3 W/m2
INTENSITY AND FREQUENCY
RELATIVE INTENSITY – DECIBEL LEVEL
Decibel level – is the
relative intensity of a
sound, determined
by relating the
intensity of a sound
wave to the intensity
at the threshold of
hearing.
Units are decibels (dB)
INTENSITY, DECIBELS AND LOUDNESS
For each 10 dB increase in the decibel level of a sound,
a sound will be approximately twice as loud.
For each 10 dB increase in the decibel level of a sound,
The intensity level of the sound is multiplied by 10.
INTENSITY, DECIBELS AND
LOUDNESS EXAMPLE
When the decibel level of traffic noise goes from
40 dB to 60 dB, how much louder does the traffic
seem? How much greater is the sound intensity?
Ans: 4 times as loud, intensity increases by a factor of 100
RESONANCE
If the driving pendulum is
set in motion, all the other
pendulums will be “forced”
into motion as well. But only
one of them will oscillate
at the same frequency as
the driving pendulum.
This is the pendulum with
the same “natural frequency”
as the driving pendulum.
RESONANCE, CONT.
When the “forced
vibration” matches the
pendulum’s natural
frequency, then the
amplitude of the
frequency will be much
larger, and the system is
in resonance.
RESONANCE AND SELF-DESTRUCTION
QUICK REVIEW – 13.1 AND 13.2
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•
•
•
•
Pitch versus frequency – musical notes
Velocity of sound in air based on air temperature
Intensity / decibel / pain chart
Doppler effect example calculation
Intensity/decibel example calculation
MUSICAL NOTES
PITCH AND FREQUENCY
TEMPERATURE EFFECT
VELOCITY OF SOUND IN AIR
v = (331 + 0.6T)
What is the velocity of sound in air at 21oC (70oF)
343.6 m/s
What is the velocity of sound in air at 38oC (100oF)
353.8 m/s
You’ll need this formula for CH13 lab !!!!!
DOPPLER EFFECT EXAMPLE
𝒗 ∓ 𝒗𝒐
fo = fs (
)
𝒗 ∓ 𝒗𝒔
fo as approaching: 2227 Hz
An ambulance races toward the scene of
an accident at 35 m/s with its siren blaring
at a frequency of 2000Hz. People in their
cars pull over and stop as the ambulance
approaches. At what frequency do they
hear the siren as the ambulance approaches
them? At what frequency do they hear it
after it passes? (Assume v = 343 m/s)
fo after passing: 1815 Hz
INTENSITY / DECIBEL / LOUDNESS
You’re sitting in the front row of a Smashin’ Pumpkins concert,
decibel level 110dB. When you get home, your mom makes
you listen to the music at a much lower level, 70dB.
How much less intense is the music at home than at the concert?
4 steps of 10dB, each a factor of 10, so 104 or10,000 times less intense
How much quieter does the music seem to you at home?
4 steps of 10dB, each half as loud, (½*½*½*½) or 1/16th as loud
13.3 HARMONICS
Standing waves
1st harmonic (f1) = “fundamental frequency”
2nd harmonic (f2) = 2 * f1
3rd harmonic (f3) = 3 * f1
nth harmonic (fn) = n * f1
HARMONICS, CONT.
Harmonics and Wavelength
For any fixed length (L), each
harmonic represents ½ wavelength
So for the 4th harmonic:
L = 4 (½ )
L = 2
=½L
HARMONICS, CONT.
Standing waves on a vibrating string:
𝒏𝒗
fn =
𝟐𝑳
fn = frequency of the nth harmonic
n = harmonic number
v = velocity of the wave on the string
L = length of the vibrating string
WAVES ON A STRING, EXAMPLE
A string on a toy guitar is 34.5cm long.
a) What is the wavelength of its first harmonic?
b) When the string is plucked, the speed of waves
on the string is 410 m/s. What are the frequencies
of the first three harmonics?
STANDING WAVES IN AN AIR COLUMN
STANDING WAVES IN AN AIR COLUMN
For pipes OPEN at both ends:
fn = (nv) / 2L
fn = frequency of the nth harmonic
n = harmonic number
v = velocity of sound in the pipe
L = length of the vibrating air column
STANDING WAVES IN AN AIR COLUMN
For pipes CLOSED at one end:
fn = (nv) / 4L
fn = frequency of the nth harmonic
n = harmonic number
v = velocity of sound in the pipe
L = length of the vibrating air column
OPEN PIPE EXAMPLE
What are the first three harmonics in a 2.45m long open pipe?
Assume that the speed of sound trough the pipe is 345 m/s.
Standing waves
on a string
Standing waves
in an open pipe
Standing waves
in a pipe closed
at one end
LAB INSTRUCTIONS
• DO NOT TAP/BANG THE TUNING FORKS
ON ANYTHING HARD!!!
• You must share the tuning forks
• Clean up your lab station when finished!
• Ok to leave the cylinder, tube, tuning forks
and mallet at the lab table
• HAND IN YOUR LAB REPORT BEFORE YOU LEAVE!!!