# Superposition Test

## Question 1

Two loudspeakers both emit sounds with a frequency of 340Hz. Both sounds have equal amplitude and phase. The amplitude is A. The speakers are 4m apart and face each other. (The speed of sound in air is 340ms^{-1})

**a)** What is the wavelength of the sound?

0.5m

1m

1.5m

2m

**b)** Ignoring the reduction of amplitude with distance from each speaker, what is the amplitude of the sound;

**i)** halfway between the speakers?

0

1 A

2 A

3.142 A

**ii)** 0.5m from either speaker?

0

1 A

2 A

3.142 A

**iii)** 1m from either speaker?

0

1 A

2 A

3.142 A

## Question 2

Two sound sources with the equal amplitudes are played over two loudspeakers. Their frequencies are 800Hz and 804Hz.

**a)** What low frequency will be heard?

0.5Hz

1Hz

4Hz

340Hz

**b)** What phenomenon is causing this?

Phase Difference

Path Difference

Constructive Interference

Beats

## Question 3

**a)** When two coherent waves combine constructively to create a maximum, what is the smallest phase difference possible in Radians?

0 Radians

0.5π Radians

1π Radians

2π Radians

**b)** What is the next biggest phase difference that would create this effect in Radians?

0 Radians

0.5π Radians

1π Radians

2π Radians

## Question 4

**a)** When two coherent waves combine destructively to create a minimum, what is the smallest phase difference possible;

**i)** in Degrees?

0 Degrees

90 Degrees

180 Degrees

360 Degrees

**ii)** in Radians?

0 Radians

1π Radians

2π Radians

3.142π Radians

**b)** What is the next biggest phase difference that would create this effect;

**i)** in Degrees?

270 Degrees

360 Degrees

450 Degrees

540 Degrees

**ii)** in Radians?

3.142π Radians

3π Radians

4π Radians

5π Radians

**c)** What happens when the two waves have a phase difference of 90 Degrees?

Something between constructive and destructive interference

Constructive interference

Destructive interference

Nothing

## Question 5

Two loudspeakers are one metre apart, and are connected to the same signal. A listener is two metres away from the left speaker on a line which is perpendicular to the line joining the two speakers (see above diagram). Speed of sound in air 340m/s.

**a)** When both speakers generate a 1000Hz signal what is the phase difference between them?

**i)** in Radians?

3.141 Radians

4.435π Radians

5.258π Radians

8.834π Radians

**ii)** in Degrees?

0 Degrees

90 Degrees

180 Degrees

360 Degrees

**b)** What is the shortest distance from the left speaker, whilst still remaining perpendicular to the line joining the two speaker (i.e. along the position line shown in the diagram below), that the listener will experience a minimum (where destructive interference is greatest)?

0m

0.971m

1.34m

2.856m

## Open Questions

For the following questions you may want to write down what you think the answers are and show them to your teacher to see if you are right.

**1** Sound from two loudspeakers connected to the same signal will form audible interference patterns. Sound from two loudspeakers connected to two different signals (such as two different pieces of music) will not form interference patterns. Why is this?

**2** Two sound sources with equal amplitudes are played over two loudspeakers. Their frequencies are 650Hz and 653Hz. Sketch a graph of pressure versus time of the combined sound for a period of 2 seconds. How might a guitarist exploit this phenomena whilst tuning their guitar?

**3** How could you use the effects of interference patterns to measure the speed of sound?