Superposition, coherence and interferenceEdexcel A-Level Physics: Subtopic test

1. 1
   Two identical loudspeakers are connected to the same signal generator, which produces a sine wave of frequency 850 Hz. They face a listener in a large room with sound-absorbing walls. The speed of sound in air is 340 m s⁻¹.

   (a)

   Which property makes the sound waves from the two loudspeakers coherent?

   [1 mark]

   • AThey have the same amplitude.
   • BThey travel at the same speed.
   • CThey are separated by exactly one wavelength.
   • DThey have the same frequency and a constant phase difference.

   (b)

   A listener is 3.60 m from one loudspeaker and 4.20 m from the other. What does the listener hear?

   [1 mark]

   • AA loud sound, because the waves are in phase
   • BA sound of double the frequency
   • CA very quiet sound, because the waves arrive in antiphase
   • DA sound of half the loudness of one speaker

   (c)

   Calculate the phase difference, in radians, between the two waves at a point where the path difference is 0.10 m.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   Two small dippers, fixed to the same motor, vibrate in a shallow tank of water at 12 Hz. Each dipper produces circular ripples that travel at 0.18 m s⁻¹. A point P on the water surface is 12.0 cm from dipper A and 15.0 cm from dipper B.

   (a)

   What is the wavelength of the ripples?

   [1 mark]

   • A1.5 cm
   • B67 cm
   • C2.2 m
   • D0.15 cm

   (b)

   What is observed at point P?

   [1 mark]

   • ADestructive interference, because the path difference is a whole number of wavelengths
   • BConstructive interference, because the path difference is exactly two wavelengths
   • CDestructive interference, because the path difference is an odd number of half-wavelengths
   • DNo interference, because the dippers have different frequencies

   (c)

   Dipper B is replaced by one that vibrates exactly in antiphase with dipper A, at the same frequency. Explain what is now observed at P.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A car radio receives a 100 MHz FM signal both directly from a transmitter and by reflection from a tall building. The speed of radio waves is 3.00 × 10⁸ m s⁻¹. At one position on the road the reflected signal has travelled 4.5 m further than the direct signal. Ignore any phase change on reflection.

   (a)

   Calculate the wavelength of the signal and the phase difference between the direct and reflected signals at this position. State the effect on the received signal.

   [3 marks]

   (b)

   Explain why the strength of the signal rises and falls as the car drives along the road, and state the path differences at which the signal is strongest.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A teacher demonstrates interference using two microwave aerials connected to the same 10.7 GHz oscillator, which gives a wavelength of 2.8 cm. A small receiver is moved along a line parallel to the line joining the aerials, beginning at the point equidistant from both aerials. Later she places two ordinary filament lamps side by side in front of a screen and sees only uniform illumination.

   (a)

   Describe and explain what the teacher observes as the receiver moves from the central point, through the first minimum, to the next maximum. Include the path differences at which these occur.

   [6 marks]

   (b)

   Explain why the two filament lamps do not produce an observable interference pattern when the microwave aerials do, and describe two ways in which a clear pattern could be obtained with light.

   [6 marks]

   Total for question 4: 12 marks

End of questions