Physics 102 Waves

Physics 102 Waves

Moza M. Al-RabbanProfessor of Physics

mmr@qu.edu.qa

Lecture 5Traveling WavesMarch 6, 2006

Lecture 5Traveling WavesMarch 6, 2006

Phase and Phase Difference The quantity 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 2 0 1 0

2 1

( ) ( )

( ) 2

kx t kx t

xk x x k x

2

x t

T

Phase difference over 2π equals space separation over .

tkx

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?

-1/ (343 m/s) /(100 s ) 3.43 mv f

/ 2 1

2 4

x

(3.43 m)0.858 m

4 4x

0.63350.043.3

60.02 rad

mm

Assess 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) -2π;(b) 0;(c) π/4;(d) π/2;(e) 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.

sound (wave speed of sound); =1.402 for airv RT

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?

-120 Hz / (343 m/s) /(20 s ) 17.2 mf v f

-1500 Hz / (343 m/s) /(500 s ) 0.690 mf v f

-120 kHz / (343 m/s) /(20,000 s ) 0.0172 mf v f

Electromagnetic Waves8

light 299,792,458 m/s 3.00 10 m/s (electromagnetic wave speed in vacuum)v c

814

-9

(3.00 10 m/s)600 nm; 5.00 10 Hz

(6.00 10 m)

cf

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?

8

8

(3.00 10 m/s)1.5 m

(2.00 10 Hz)

c

f

11

8

(8.0 10 m)2,700 s 45 min

(3.00 10 m/s)

xt

c

Index of Refraction

speed of light in vacuum

speed of light in material

cn

v

vacmat

mat mat vac

v c c

f nf nf n

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:

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?

glass vac1.50; 600 nmn

88

glassglass

(3.00 10 m/s)2.00 10 m/s

(1.50)

cv

n

-7vacglass

glass

(600 nm)400 nm 4.00 10 m

(1.50)n

-3

-7glass

(1.00 10 m)2,500

(4.00 10 m)

dN

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 IntensityPower and Intensity

Intensity: I = P/a (units – W/m2)

The power of a wave is the rate, in joules per second, at which the wave transfers energy.

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?

-32

2 -3 2

(1.0 10 W)1,270 W/m

(0.5 10 m)

P PI

a r

Inverse Square Law

sphere

2 (intensity for spherical waves)

4

PIa

P

r

2 21 1 2

2 22 2 1

/ 4

/ 4

I P r r

I P r r

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 inverse-square law because of the many reflecting surfaces.

Inverse Square Law

2 ( is a constant)I CA C

The intensity of a wave is proportional to the square of its amplitude.

1 22

E kA

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

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

Chapter 20 - Summary (1)

Chapter 20 - Summary (2)

Chapter 20 - Summary (3)

End of Lecture 4End of Lecture 4