Chapter 12
SOUND
SOUND
SOUND
• Sound Waves are longitudinal waves: The
particles of the medium through which it
propagates oscillates in the same direction
along which the waves travel.
• Vibrating objects produce sound: guitar
strings, speakers etc.
• Speaker cones produce pressure variations by
displacing air molecules from a uniform
distribution.
• Rarefactions (relaxed) and compression
regions are formed.
Sound Wave Generated by a Loudspeaker
Frequency Ranges
• Velocity of wave: v = f.
• The human ear can respond to only a limited
range of sound frequency – called the audible
range: 20 Hz to 20 kHz.
• Ultrasound – beyond 20 kHz, Infrasound –
below 20 Hz.
• Animals can detect sound beyond the audible
range: Dolphins can pick sound at 250 kHz.
Dogs can pick sound at 50 kHz. Elephants
communicate using sound waves at 10 Hz.
Frequency Ranges
• The speed of sound differs in different media.
• Also speed depends on temperature (v T)
Medium
Air
Carbon dioxide CO2
Hydrogen (H2)
Mercury (25oC)
Water (25oC)
Concrete
Granite
Speed (m/s)
331
259
1,284
1,450
1,493
3,100
6,500
Loudness
• Loudness of sound is related to amplitude of
the sound wave – maximum displacement of
the medium particles.
• All things being equal, larger amplitude
means louder sound.
• Intensity (I) of sound is defined as the
average power of the wave per unit area.
• I = power/area = P/4r2
• SI unit of intensity is watts/m2 (W/m2).
• The wave traveling in all directions.
Loudness
• Intensity  (amplitude)2.
• Louder sound has larger amplitude or larger
intensity.
Example
• If at 30 m, the intensity of a sound is 100
W/m2, what will the intensity be at 300 m
away?
I  1/r2 OR I1r12 = I2r22
I2 = (I1r12)/r22
I2 = (100 x 30 x 30)/3002 = 1 W/m2
Intensity
• Louder sound has larger amplitude or larger
intensity.
• Perception of loudness by the human ear
varies logarithmically with intensity of
sound ie, Loudness  Log of Intensity.
• The lowest intensity of sound that can be
detected by the human ear is called the
threshold of hearing and is equal to
Io = 10-12 W/m2.
Decibels
• Sound intensity level () in units of
decibels (dB) is defined as the log10 of the
ratio of a sound intensity to the threshold
intensity, Io.
 = (10dB)log10(I/Io).
• 0 dB = threshold of hearing.
• If a sound has intensity of 10-5 W/m2, its
intensity level is
 = 10dBlog10(10-5/10-12)
= 10log10(107) = 10 x 7 = 70 dB.
Logarithms
•
•
•
•
•
Log101 = Log10100 = 0
Log1010 = Log10101 = 1
Log10100 = Log10102 = 2
Log10(a/b) = Log10(a) – Log10(b)
Log10(ab) = Log10(a) + Log10(b)
Example
• If at 30 m, the intensity of a sound is 100
W/m2, what is the sound intensity level at
this distance?
 = (10dB)log10(I/Io).
 = (10dB)log10(102/10-12).
= (10dB)log10(1014).
 = 140 dB
Decibels
• If 1 person can shout with loudness 50 dB.
How loud will it be when 100 people shout?
1) 52 dB
2) 70 dB
3) 150 dB
1 = (10 dB) log10(I1/I0)
100 = (10 dB) log10(I100/I0)
100 – 1 = (10 dB) log10(I100/I1)
100 = 50 + (10 dB) log10(100/1)
100 = 50 + 20
Intensity
• Recall Intensity = P/A. If you are standing 6
meters from a speaker, and you walk towards
it until you are 3 meters away, by what factor
has the intensity of the sound increased?
1) 2
2) 4
3) 8
Area goes as d2 so if you are ½ the distance the
intensity will increase by a factor of 4
Suppose you are standing a distance D away from a
speaker that is radiating sound in a spherically
uniform way. You walk away from the speaker until
the loudness of the sound is reduced by a factor of
two. About how far from the speaker are you now?
(neglect any reflections from the ground)
1. 10D
2. 4D
3. 3D
4. 2D
A hiker determines the length of a
lake by listening for the echo of her
shout reflected by a cliff at the far
end of the lake. She hears the echo
1.5 s after shouting. Estimate the
length of the lake. [Use v = 330 m/s]
What is the intensity of sound
at the pain level of 120 dB?
Compare it to that of a whisper
at 46 dB.
Human beings can typically detect
a difference in sound intensity
level of 2.0 dB. What is the ratio of
the amplitudes of two sounds
whose levels differ by this
amount?
Examples
Noise produced by an engine has a sound level
of 200 dB when measured at 50 m from the
source. At this location, what is the intensity
of this noise?
(A) 108 W/m2 (B) 10-10 W/m2
W/m2
(D) 10-8 W/m2
(E) 143 W/m2
(C) 14.3
Examples
Which of the following statements is correct?
(A) Sound is an example of transverse waves.
(B) The threshold of hearing is the lowest
frequency a normal human ear can detect.
(C) At the threshold of hearing, the sound
intensity level is 0 dB.
(D) The audible range is a range of intensities a
normal human ear can detect.
(E) The intensity of sound will increase if you
increase your distance from the source of the
sound.
Examples
The intensity of a sound 20 m away from
the source is 85.0 W/m2. What is the
sound intensity level, , at this distance?
(A) 320.7 dB
(B) 100.1 dB (C)
13.93 dB (D) 139.3 dB
(E) 1,393
dB
If the intensity of a sound source
is doubled, by how much will the
sound intensity level increase?
If the intensity of a sound source
is doubled, the sound intensity
level will increase by 3 dB.
Adding 3 dB to a sound intensity
level doubles its intensity.
If the intensity of a sound source
is increased by a factor of ten, by
how much will the sound intensity
level increase?
If the intensity of a sound source
is increased by a factor of 10, the
sound intensity level will increase
by 10 dB.
Adding 10 dB to a sound intensity
level raises its intensity ten times.
An unfingered guitar string is 0.70 m
long an is tuned to play E above
middle C (330 Hz). How far from the
end of this string much the finger be
placed to play A above middle C (440
Hz)?
• Pitch of sound (high or low)
corresponds to frequency.
• High pitch = high frequency.
• Low pitch = low frequency.
Pitch  log10(f), i.e. pitch is a
logarithmic function of frequency.
A sound wave having frequency f0, speed v0 and
wavelength 0, is traveling through air when in
encounters a large helium-filled balloon. Inside the
balloon the frequency of the wave is f1, its speed is
v1, and its wavelength is 1 Compare the frequency
of the sound wave inside and outside the balloon
1. f1 < f0
2. f1 = f0
3. f1 > f0
f
0f1
A sound wave having frequency f0, speed v0 and
wavelength 0, is traveling through air when in
encounters a large helium-filled balloon. Inside the
balloon the frequency of the wave is f1, its speed is
v1, and its wavelength is 1.
Compare the speed of the sound wave inside and
outside the balloon.
1. v1 < v0
2. v1 = v0
3. v1 > v0
V0=343m/sV1=965m/s
A sound wave having frequency f0, speed v0 and
wavelength 0, is traveling through air when in
encounters a large helium-filled balloon. Inside the
balloon the frequency of the wave is f1, its speed is
v1, and its wavelength is 1 Compare the
wavelength of the sound wave inside and outside
the balloon
1. 1 < 0
1
0
2. 1 = 0
3. 1 > 0
=v/f
Standing Waves
• Recall for string
– Node at each end
– Standing wave n = 2L/n
– or fn = n v/(2L) = nf1
Standing Waves
For Pipe open at both ends
– Pressure node at each end
– Standing wave n = 2L/n or fn = n v/(2L)
• For Pipe open at one end, pressure node
at one end anti node at other.
– Standing wave n = 4L/n or fn = n
v/(4L) n =1, 3, 5.. Or fn = nf1
Resonance
• What happens to the fundamental
frequency of a pipe, if the air (v=300
m/s) is replaced by helium (v=900
m/s)?
1) Increases 2) Same 3) Decreases
f = v/(4L)
THE END
Intensity and Loudness
• Intensity if the power per unit area.
–I = P / A
–Units Watts/m2
• For Sound Waves
–I = p02 / (2 r v)
–Proportional to p02 note Energy goes as A2
• Loudness (Decibels)
–Loudness perception is logarithmic
–Threshold for hearing I0 = 10-12 W/m2
 = (10 dB) log10 ( I / I0)
2 – 1 = (10 dB) log10(I2/I1)
Speaker radiating power P
Changing I by 10 will change
loudness by 2 (pg 412 in text)
I1 = P/(4D12)
D1
I2 = P/(4D22)
We want I1/I2 = 10
D2
I1
P

I 2 4D12
P
D22
 2
2
4D2 D1
D2  10D1  3.16 D1
D22
 10
2
D1
Preflight 5
• As a police car passes you with its siren
on, the frequency of the sound you hear
Doppler Example Audio
from its siren
Doppler Example Visual
1) Increases
2) Decreases
3) Same
Doppler Effect moving source
• When source is coming toward you
– Distance between waves decreases
– Frequency increases
• When source is going away from you
– Distance between waves increases
– Frequency decreases
• fo = fs / (1- vs/v)
Doppler Effect moving observer
• When moving toward source
– Distance between waves decreases
– Frequency increases
• When away from source
– Distance between waves increases
– Frequency decreases
• fo = fs (1- vo/v)
Combine: fo = fs (1-vo/v) / (1-vs/v)
Doppler
A: You are driving along the highway at 65 mph, and behind you a
police car, also traveling at 65 mph, has its siren turned on.
B: You and the police car have both pulled over to the side of the
road, but the siren is still turned on.
In which case does the frequency of the siren seem higher to you?
f
f’
1. Case A
v
2. Case B
correct
3. same
vs
vo
vo
1
f'
v

f 1  vs
v
Pg 427