Wave

Interference

Superposition of Waves

• when two or more waves meet, the waves

will combine to give a resultant wave

• the amplitude of the resultant wave will be

the vector sum of the separate

displacements (Principle of Superposition)

• superposition will occur for all types of

waves (sound, light, water waves, etc.)

• the two waves will continue to move

independently of each other

• when two waves meet in phase, constructive

interference will occur (amplitudes add)

• when out-of-phase waves meet, destructive

interference occurs

Destructive interference

(different A)

Wave 1

Wave 2 - - - -

Wave 1 + Wave 2

Interference of 2 different

•Waves A and B have slightly different wavelengths.

•The thick curve

in C is the

superposition of

A and B. An

interference

(beat) is seen in

the curve C.

Constructive and destructive interference is occuring

The red line is the sum of these two.

The height of the bow wave is reduced, which reduces the hull

drag caused by the bow wave. This improves fuel economy,

and increases range.

•the green line is

the natural bow

wave of the hull.

•The blue line is

the wave created

by the protruding

bulb.

Standing Waves

• A string fixed at both ends can vibrate at

certain frequencies (resonate frequencies)

• A standing wave is a wave that doesn’t

appear to be moving

• Standing waves are formed when two waves of

the same frequency moving in opposite

directions interfere

• A wave will reflect off the fixed end and interfere with the incident wave

• If the length and frequency are correct, standing waves result

• Ropes can vibrate at more than 1 frequency

• Points of destructive

interference are called

nodes (no displacement

of the medium)

• The points of constructive

interference are called

antinodes (maximum

displacement of the

medium)

• Nodes occur every ½

wavelength

• Fundamental (lowest freq., ½ )

• 2nd harmonic (2x fund., 1 1st overtone)

• 3rd harmonic (3x fund., 3/2 2nd overtone)

Standing waves on a vibrating metal

sheet

• The salt collects where the sheet is not

vibrating (nodes)

Interference Patterns

• When 2 in-phase

waves from

different sources

meet, interference

patterns are

formed

2 Wave Sources

• interference

occurs because

the waves from

each source

travel a different

distance and

arrive at a point

either in phase

or out of phase

Diffraction

• diffraction is the bending of waves as they

pass through an opening

• the amount of diffraction depends on the

ratio of wavelength to width of opening

• long waves diffract more than short waves

• sound is diffracted around corners more than

light

• If is much smaller than the opening, very little diffraction occurs

• If is much larger than the opening, lots of diffraction occurs

• when waves pass through two openings,

diffraction occurs and the diffracted waves

interfere

• When a red laser beam is passed through 2

narrow slits, the light waves diffract. Predict what

will be seen on the screen.

Example

• Two loudspeakers are

emitting 107 Hz in

phase. They are set

up as shown. The

speed of sound is 343

m/s. Will the person

hear a loud sound or

a quiet sound?

Refraction

• Refraction occurs when a wave moves from one medium into another with a different speed

• If the wave enters the new medium at angle to the normal, the wave will change direction

• The refracted wave will have the same

frequency but a different speed and

wavelength

• If the refracted wave slows down, it will

bend towards the normal

• If the refracted wave speeds up, it will

bend away from the normal

Red areas are due to red light refracting through

Earth’s atmosphere (long waves refract less than

short waves)