Topic 2 - Interference, Diffraction & Resonance

What is the principle of linear superposition?

When two or more waves are present simultaneously at the same place, the resultant disturbance is the sum of the disturbances from the individual waves.

What is constructive interference in sound waves?

When two waves always meet condensation-to-condensation and rarefaction-to-rarefaction, they are exactly in phase and exhibit constructive interference.

What is destructive interference in sound waves?

When two waves always meet condensation-to-rarefaction, they are exactly out of phase and exhibit destructive interference.

What types of waves can exhibit interference?

• Sound waves

• Waves on a string

• Electromagnetic waves

• Other wave types

What is diffraction?

Diffraction is the bending of a wave around an obstacle or the edges of an opening.

When does diffraction occur strongly?

When the wavelength and the opening have similar dimensions.

What happens in diffraction through a slit opening?

• Waves bend around the opening

• Interference occurs between wavelets from different points in the opening

What feature is mentioned for a single slit diffraction pattern?

First minimum.

What is mentioned about diffraction through a circular opening?

It produces a diffraction pattern with a first minimum.

Example problem given in the slides?

A speaker with a 12 cm diameter plays sounds of approximately 4000 Hz.
Listeners sit on a 2 m long couch, 3 m away from the speaker.
Speed of sound in air = 340 m/s.

What happens when a wave reflects from a wall?

A forward-traveling half-cycle becomes a backward-traveling half-cycle that is inverted.

What happens if the timing is not correct during reflection?

The newly formed and reflected cycles tend to offset one another.

What causes a large amplitude standing wave to develop?

Repeated reinforcement between newly created and reflected cycles.

What is resonance?

The build-up of amplitude through repeated reinforcement.

At what frequencies does resonance occur?

At specific frequencies called the natural frequencies of the system.

What is a node in a standing wave?

A position where the amplitude is zero.

What is an antinode in a standing wave?

A position where the amplitude is maximum.

What is the distance between two nodes or two antinodes?

Half a wavelength (λ/2).

What type of standing wave is mentioned?

Longitudinal standing wave.

What system is used as an example for transverse standing waves?

A system closed (clamped) at both ends.

What determines the wavelength in resonant systems?

The dimensions of the system determine the wavelength.

What determines the frequency of resonance?

The speed of sound in the system.

What example is given involving a flute?

When all holes are closed on a flute, the lowest note is middle C (261.6 Hz).
Speed of sound = 340 m/s.
The flute is assumed to be a cylinder open at both ends.
Find the distance L.

What additional system type is mentioned for standing waves?

Tube closed at one end.