Chapter 15

Wave Motion

Section 15-1: Simple Wave Motion

Transverse and Longitudinal Waves

A transverse wave

The oscillation of a transverse wave is perpendicular to the wave motion.

A longitudinal wave

The oscillation of a spring is parallel to the motion

Wave pulses

A wave pulse is a travelling disturbance.

The speed of waves

The speed of a wave is a property of the medium in which it travels.

In a stretched string v= (F/μ)½

In a fluid v= (B/ρ)½

And in a gas v=(γRT/M)½

The are called the dispersion relations for the media.

The derivation of v for waves on a string

The Wave Equation

ð2y/ðx2 = (1/v2) ð2y/ðt2

Here y represents the vertical displacement of the string. It is called the wave function

Section 15-2: Harmonic Waves

Harmonic waves on a string have a wave function of the form y=Asin(kx-ωt+φ).

The Energy of Waves on a String

Harmonic Sound Waves

Sound waves have a wave

function of the form:

s=s0sin(kx-ωt) where s

represents the horizontal

displacement of the wave.

The Energy of Sound Waves

Electromagnetic Waves: These will be studied in Phy 2049

Section 15-3: Waves in Three Dimensions

Circular wavefronts

Sound waves from a telephone handset.

At a great distance from the source, spherical wavefronts look like parallel planes called plane waves

A two dimensional analog to plane waves

Wave Intensity

Wave intensity is the radiated power per unit area of the wavefront.

Intensity Level and Loudness: This would be equivalent to brightness in a light wave.

β = 10 log (I/I0) in decibels (dB). I0 is the threshold of hearing= 1x10-12 watts/m2

Section 15-4: Waves Encountering Barriers

Reflection and Refraction: Reflection is the “bouncing” of a wave incident on an interface, back into the same medium

Refraction is the “bending” of the path of a light ray as it travels from one medium into another. This is due to a difference in wave speed between the two media.

Total Internal Reflection is when an incident ray is totally internally reflected. This occurs when the angle of incidence is a critical value.

A wave from a light string encountering a heavier string (for which the speed is lower) suffers a phase change of π upon reflection.

A wave from a heavy string encountering a lighter string (for which the speed is higher) suffers no phase change.

Tunneling is when a wave penetrates through a barrier.

Diffraction: The ability of a wave to move around an obstacle in its path.

Waves in a ripple tank encountering a wall with a slit. If the slit width is small compared to λ, the waves move in around the barrier and the slit becomes a point source.

If the slit width is large compared to λ, there is very little diffraction.

Transmitted waves radiate widely as they pass through a slit. The slit acts as a point source.

Transmitted particles are confined to narrow angle.

Sound waves can give images, just like light.

Section 15-5: The Doppler Effect

The Doppler Effect is a shift in frequency of a wave when there relative motion between the source and the observer. The shift is toward higher frequencies (shorter wavelengths) when the source and observer are approaching, and to lower frequencies (longer wavelengths) when they are receding.

Shock Waves

When the source is traveling faster than the speed of the sound wave in the medium, shock waves result when the waves interfere with each other.

This is the reason for the “sonic boom” produced by jets that exceed the sound barrier.

This is “bow shock”.

When applied to electromagnetic waves, this is called the Cerenkov Effect.