Transcript Physics 102 Waves - Qatar University

Physics 102
Waves
Lecture 5
Traveling Waves
March 6, 2006
Moza M. Al-Rabban
Professor of Physics
[email protected]
Phase and Phase Difference
The quantity kx  t    is called the
phase of the wave. The wave fronts we have
seen in the previous figures are surfaces of
constant phase because each point on such a
surface has the same displacement, and therefore
the same phase. The displacement can be written
as D(x,t) = Asin().
The figure shows a snapshot of a traveling
wave. The phase difference between points x1
and x2 is:
  2  1  (kx2  t  0 )  (kx1  t  0 )
 k ( x2  x1 )  k x  2
x

 x
t


2

T
Phase difference over
2π equals space
separation over .
Example 6: The Phase Difference between
points of a Sound Wave
A 100 Hz sound wave travels at 343 m/s.
(a) What is the phase difference between two points 60 cm apart in the direction the
wave is traveling?
(b) How far apart are two points with phase difference 900?
  v / f  (343 m/s) /(100 s-1 )  3.43 m
0.60m
  2
 0.350 rad  63.0
3.43m
 /2 1



2
4
x
x 

4

(3.43 m)
 0.858 m
4
Assess The phase difference increases as x increases, so we
expect the answer to part b to be larger than 60 cm.
Clicker Question 1
What is the phase difference between the crest of a wave and the
adjacent trough?
(a)
(b)
(c)
(d)
(e)
-2π;
0;
π/4;
π/2;
π.
Longitudinal Waves
Longitudinal waves (e.g., sound) are produced in a compressible medium by
longitudinal motion of each particle of the medium, participating in the wave motion
by moving in a horizontal path as the wave propagates. This produces moving regions
of compression and rarefaction in the medium.
Note that although the wave moves to the right, the individual particles return to
their original positions.
vsound   RT
(wave speed of sound);  =1.402 for air
Sound Waves
We usually think of sound waves as traveling
through air, but actually sound can travel
through any gas liquid, or solid. The figure
shows sound as traveling regions of
compression and rarefaction, traveling out from
a loudspeaker as a longitudinal wave.
Sound waves in gases and liquids are always
longitudinal, but sound in solids can be both
longitudinal compression waves and transverse
“shear” waves, which usually travel at differing
speeds in the medium.
We hear sound in the range of 20 Hz to 20
kHz, but sound waves at higher and lower
frequencies are common.
Example: Sound Wavelengths
What are the wavelengths of sound waves at the limits of human hearing and at
the midrange frequency of 500 Hz?
f  20 Hz   v / f  (343 m/s) /(20 s-1 )  17.2 m
f  500 Hz   v / f  (343 m/s) /(500 s-1 )  0.690 m
f  20 kHz   v / f  (343 m/s) /(20,000 s-1)  0.0172 m
Electromagnetic Waves
vlight  c  299,792,458 m/s  3.00 108 m/s (electromagnetic wave speed in vacuum)
(3.00 108 m/s)
14
  600 nm; f  

5.00

10
Hz
-9
 (6.00 10 m)
c
Example:
Traveling at the Speed of Light
A satellite exploring Jupiter transmits data to the Earth as a radio wave with a
frequency of 200 MHz.
What is the wavelength of the electromagnetic wave?
How long does it take for the signal to travel 800 million km from Jupiter to
Earth?
c (3.00 108 m/s)
 
 1.5 m
8
f (2.00 10 Hz)
x
(8.0 1011 m)
t 

 2,700 s  45 min
8
c (3.00 10 m/s)
Index of Refraction
Typically, light slows down when it passes through a transparent material like
water or glass. The slow-down effect is characterized by the index of refraction of
the material:
n
speed of light in vacuum c

speed of light in material v
mat 
v
f mat


c
c

 vac
nf mat nf vac
n
Example:
Light Traveling through Glass
Orange light with wavelength 600 nm is incident on a 1 mm thick microscope
slide.
(a) What is the speed of light in the glass?
(b) How many wavelengths of light are inside the slide?
nglass  1.50; vac  600 nm
vglass 
glass 
N
nglass
(3.00 108 m/s)

 2.00 108 m/s
(1.50)
vac

c
nglass
d
glass
(600 nm)
 400 nm  4.00 10-7 m
(1.50)
(1.00 10-3 m)

 2,500
-7
(4.00 10 m)
Clicker Question 2
Which inequality describes the three indices of refraction?
•
•
•
•
•
n1 > n2 > n3;
n1 > n2 > n3;
n2 > n1 > n3;
n1 > n3 > n2;
n3 > n1 > n2;
Power and Intensity
The power of a wave is the rate, in joules per second, at
which the wave transfers energy.
Intensity: I = P/a (units – W/m2)
Example:
Intensity of a Laser Beam
A red helium-neon laser emits 1.0 mW of light power in a laser beam that is
1.0 mm in diameter.
What is the intensity I of the laser beam?
P
P
(1.0 10-3 W)
2
I  2

1,
270
W/m
a r
 (0.5 10-3 m)2
Inverse Square Law
I

P
asphere
P
(intensity for spherical waves)
4 r 2
I1 P / 4 r12 r22

 2
2
I 2 P / 4 r2 r1
Wave intensities are strongly affected
by reflections and absorption. So these
Equations apply to situation such as
light from a star or the sound from a
firework exploding high in the air. Indoor
sound does not obey a simple inversesquare law because of the many
reflecting surfaces.
Inverse Square Law
For a sinusoidal wave, each particle in the medium oscillates back and forth in
simple harmonic motion.
A particle in SHM with amplitude A has energy
E  12 kA2
Where k is the spring constant of the medium, not the wave number.
It is this oscillatory energy of the medium that is transferred, particle to particle,
as the wave moves through the medium.
Because a wave’s intensity is proportional to the rate at which energy is
transferred through the medium, and because the oscillatory energy in the
medium is proportional to the square of the amplitude, we can infer that for any
wave
I  CA2 (C is a constant)
The intensity of a wave is proportional to the square of its amplitude.
Chapter 20 - Summary (1)
Chapter 20 - Summary (2)
Chapter 20 - Summary (3)
End of Lecture 4