1. No category

General Physics II
Sound
Sound...
...a longitudinal wave in air caused by a vibrating
object.
Large scale - swinging door creates macroscopic
currents
Small scale - tuning fork creates sound waves
Page 1
Series of condensations (increased pressures) and
rarefactions (decreased pressures)
Range of Sound
infrasonic
frequencies < 20 Hz
ultrasonic
frequencies > 20,000 Hz
human hearing range
frequencies between 20 Hz and 20,000 Hz
Page 2
Speed of Sound
Liquids and Gases: B is bulk
modulus, ρ is mass/volume
Solids: Y is Young’s modulus
vair varies with the air
temperature:
v=
v=
v air = 331 m s 1 +
B
ρ
Y
ρ
TC
273 .15
Interference of Sound Waves
Assume sources “a” and “b” are “coherent”. If
observer is located ra and rb from the two sources,
Source a
Source b ra − rb = nλ for maximum
ra − rb = (n + 1 2)λ for minimum
ra
rb
f beat = f a − f b
Observer
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DOPPLER EFFECT
•
A change in the frequency experienced by an observer due
to motion of either the observer or the source.
"Wheeeeeeeeeeee…….Oooooooooooooo”
Examples:
moving cars and trains
moving buzzer in a ball (in class demo)
rotating whistle
Higher frequency: Object approaching
Lower frequency: Object receding
STATIONARY
MOVING
SOUND-GENERATING OBJECT
SOUND-GENERATING OBJECT
Velocity, v
A
Waves are created at point
source and radiate outward
creating a wave front with the
same frequency as that of the
source.
B
Although the frequency of the
sound generating object remains
constant, wave fronts reach the
observer at Point B more
frequently than Point A.
Page 4
http://www.kettering.edu/~drussell/Demos/doppler/doppler.html
Doppler Effect, Moving Observer
When not moving, f = v
λ
v + vo 
 v 
When moving towards, ƒ ' = ƒ 
Fig 14.8, p. 435
Slide 12
Page 5
If observer moves away:
 v − vo 
ƒ' = ƒ
 v 
Fig 14.9, p. 436
Slide 13
The Source in Motion
Approaching source:
f'= f
v
v − vs
Source leaving:
f'= f
v
v + vs
Page 6
Doppler Effect:
Both Observer and Source Moving
O Toward
f'= f
O Away
v ± vo
v m vs
S Toward
S Away
Switch appropriate signs if observer
or source moves away
A train has a whistle with a
frequency of a 1000 Hz, as
measured when the both the
train and observer are
stationary. For a train moving
in the positive x direction,
which observer hears the
highest frequency when the
train is at position x=0.
Observer A has velocity VA>0 and has position XA>0.
Observer B has velocity VB>0 and has position XB<0.
Observer C has velocity VC<0 and has position XC>0.
Observer D has velocity VD<0 and has position XD<0.
Page 7
Standing Waves
Standing Waves:
Resultant wave created by the interference of two waves
traveling at the same frequency, amplitude and wavelength
in opposite directions.
Standing Waves have Nodes and Antinodes
Nodes:
Points in the standing wave where the two waves
cancel – complete destructive interference–
creating a stationary point!
Antinodes
Point in the standing wave, halfway between the
nodes, at which the largest amplitude occurs.
Standing Waves on a String
Wavelength, λ
λ2 = L
Only certain
frequencies of
vibration produce
standing waves
for a given string
length!!!
λ3 = 2L/3
The wavelength of
each of the
standing waves
depends on the
string length, L
λ1 = 2L
λn = 2L/n
λ4 = 2L/4 or ½ L
Page 8
Only certain frequencies of vibration
produce standing waves for a given string
length!!!
fn = n v/2L n = 1, 2, 3, …
Where,
v is the speed of waves on the vibrating string
(NOT the speed of the resultant waves in air!!!!)
L is the portion of the string that is vibrating
Standing Waves on a String
Frequency, f
A
N
N
f1 = v / λ1
A
N
A
N
N
Fundamental
Frequency or
1st Harmonic
2nd Harmonic
f2 = 2 f1
A
A
N
N
N
3rd Harmonic
N
A
A
A
N
N
f3 = 3 f1
A
N
A
N
f4 = 4f1
N
Page 9
4th Harmonic
Standing Waves in an Air Column
A node for displacement is always an antinode for pressure and vice
versa, as illustrated below. When the air is constrained to a node, the air
motion will be alternately squeezing toward that point and expanding
away from it, causing the pressure variation to be at a maximum.
Tube Closed at One End
Wavelength, λ
Frequency, f
λ1 = 4L
f1 = v / λ1
Fundamental
Frequency or
1st Harmonic
λ3 = 4L/ 3
f3 = 3 f1
3rd Harmonic
λ5 = 4L/5
f5 = 5 f1
5th Harmonic
λn = 4L/n
Page 10
fn = n v/4L n = 1, 3, 5,…
Tube Open at Both Ends
Wavelength, λ
Frequency, f
Fundamental
f1 = v / λ1 Frequency or
λ1 = 2L
1st Harmonic
λ2 = L
f2 = 2 f1
2nd Harmonic
λ3 = 2L/3
f3 = 3 f1
3rd Harmonic
λn = 2L/n
fn = n v/2L n = 1, 2, 3, …
End of
Sound
Lecture
Page 11