Transcript Physics 106P: Lecture 1 Notes

Physics 101: Lecture 27
Sound

Today’s lecture will cover Textbook Sections 16.1 - 16.10
UB, Phy101: Chapter 16, Pg 1
What is a wave ?
DEMO


According to our text:
A wave is a traveling disturbance that transports
energy
Examples:
Sound waves (air moves back & forth)
Stadium waves (people move up & down)
Water waves (water moves up & down)
Light waves (what moves ??)
UB, Phy101: Chapter 16, Pg 2
Types of Waves


Transverse: The medium oscillates perpendicular to the
direction the wave is moving.
Water (more or less)
Slinky
Longitudinal: The medium oscillates in the same
direction as the wave is moving
Sound
Slinky
UB, Phy101: Chapter 16, Pg 3
Wave Properties


Wavelength: The distance  between identical points on the wave.
Amplitude: The maximum displacement A of a point on the wave.
Wavelength

Amplitude A
A
UB, Phy101: Chapter 16, Pg 4
Wave Properties...


Period: The time T for a point on the wave to undergo one
complete oscillation.
Speed: The wave moves one wavelength  in one period T
so its speed is v = / T.
v

T
UB, Phy101: Chapter 16, Pg 5
v=/T

Wave Properties...
The speed of a wave is a constant that depends only on the medium,
not on amplitude, wavelength or period (similar to SHM)
 and T are related !

=vT
or  = 2 v / (since T = 2 / 
or  v / f

(since T = 1/ f )
Recall f = cycles/sec or revolutions/sec
 2f
UB, Phy101: Chapter 16, Pg 6
Preflight 1
Suppose a periodic wave moves through some medium. If the period of the wave
is increased, what happens to the wavelength of the wave assuming the speed of
the wave remains the same?
correct
1. The wavelength increases
2. The wavelength remains the same
3. The wavelength decreases
UB, Phy101: Chapter 16, Pg 7
Preflight 2
The speed of sound in air is a bit over 300 m/s, and the speed of light in air is
about 300,000,000 m/s. Suppose we make a sound wave and a light wave that
both have a wavelength of 3 meters. What is the ratio of the frequency of the
light wave to that of the sound wave?
correct
1. About 1,000,000.
2. About 1,000.
2. About .000,001
f = v/
fL/fS = vL/vS = 1,000,000
fS = 100 Hz
(~ really low G)
fL = 100 MHz (FM radio)
UB, Phy101: Chapter 16, Pg 8
Preflight 3 & 4
Suppose that a longitudinal wave moves along a Slinky at a speed of 5
m/s. Does one coil of the slinky move through a distance of five
meters in one second?
1. Yes
2. No
correct
no single coil on the slinky will move anywhere
near 5 meters. Rather many coils will move many
smaller distances in shorter times to create the
wave that has a speed of 5 meters per sec.
5m
UB, Phy101: Chapter 16, Pg 9
Another Question

The wavelength of microwaves generated by a microwave oven
is about 3 cm. At what frequency do these waves cause the
water molecules in your burrito to vibrate ?
(a) 1 GHz
(b) 10 GHz
(c) 100 GHz
1 GHz = 109 cycles/sec
The speed of light is c = 3x108 m/s
UB, Phy101: Chapter 16, Pg 10
Another question, ans.

Recall that v = f.
v 3  10 8 m s
f  
 1010 Hz  10GHz

.03m
H
H
Makes water molecules wiggle
O
1 GHz = 109 cycles/sec
The speed of light is c = 3x108 m/s
UB, Phy101: Chapter 16, Pg 11
Visible
Absorption coefficient
of water as a function
of frequency.
f = 10 GHz
“water
hole”
UB, Phy101: Chapter 16, Pg 12
Waves on a String
T
T
v

m/L

UB, Phy101: Chapter 16, Pg 13
Preflights 5 & 6
A rope of mass M and length L hangs from the ceiling with nothing attached to
the bottom (see picture). Suppose you start a transverse wave at the bottom
end of the rope by giggling (sic) it a bit. As this wave travels up the rope its
speed will:
correct
1. Increase
2. Decrease
3. Stay the same
v
the tension gets greater as you go up
UB, Phy101: Chapter 16, Pg 14
Preflight
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
correct
3. f1 > f0
f0 f1
UB, Phy101: Chapter 16, Pg 15
Preflight
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
correct
V0=343m/s
V1=965m/s
UB, Phy101: Chapter 16, Pg 16
Preflight
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
2. 1 = 0
3. 1 > 0
correct
0
1
=v/f
UB, Phy101: Chapter 16, Pg 17
Doppler Effect DEMO
UB, Phy101: Chapter 16, Pg 18
UB, Phy101: Chapter 16, Pg 19
UB, Phy101: Chapter 16, Pg 20
UB, Phy101: Chapter 16, Pg 21
Preflight
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?
1. Case A
f
f’
2. Case B
v
3. same
correct
vs
vo
vo
f'
v

f 1  vs
v
1
Pg 479
NOT ON EXAM
UB, Phy101: Chapter 16, Pg 22
Interference and Superposition
Constructive interference
Destructive interference
UB, Phy101: Chapter 16, Pg 23
Superposition & Interference


Consider two harmonic waves A and B meeting at x=0.
Same amplitudes, but 2 = 1.15 x 1.
The displacement versus time for each is shown below:
A(1t)
B(2t)
What does C(t) = A(t) + B(t) look like??
UB, Phy101: Chapter 16, Pg 24
Superposition & Interference


Consider two harmonic waves A and B meeting at x = 0.
Same amplitudes, but 2 = 1.15 x 1.
The displacement versus time for each is shown below:
A(1t)
B(2t)
C(t) = A(t) + B(t)
DESTRUCTIVE
INTERFERENCE
CONSTRUCTIVE
INTERFERENCE
UB, Phy101: Chapter 16, Pg 25
UB, Phy101: Chapter 16, Pg 26
Beats
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Can we predict this pattern mathematically?
 Of course!
Just add two cosines and remember the identity:
A cos( 1t )  A cos( 2 t )  2 A cos L t  cos H t 
where  L 
1
1   2 
2
and
H 
1
1  2 
2
cos(Lt)
UB, Phy101: Chapter 16, Pg 27
Standing Waves:
HW: Airport
Fixed “nodes”
UB, Phy101: Chapter 16, Pg 28
Standing Waves:
L  / 2
f1 = fundamental frequency
(lowest possible)
v
F

f = v / tells us f if we know v and 
L 
f2 = first overtone
UB, Phy101: Chapter 16, Pg 29