Superposition, interference and path differenceEdexcel International A Level Physics: Subtopic test

1. 1
   Two small loudspeakers, X and Y, are connected to the same signal generator and emit sound of wavelength 0.40 m in phase. A listener stands at a point P that is 3.00 m from X and 3.60 m from Y.

   (a)

   What is the path difference at P between the waves from X and Y?

   [1 mark]

   • A6.60 m
   • B0.60 m
   • C1.5 m
   • D0.24 m

   (b)

   What does the listener hear at P?

   [1 mark]

   • AA loud sound, because the path difference is a whole number of wavelengths
   • BA loud sound, because the path difference is greater than one wavelength
   • CA quiet sound, because the waves arrive in antiphase
   • DA sound as loud as that from one speaker alone

   (c)

   Explain, using ideas of path difference and phase, why the sound at P is not loud.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A progressive wave has a wavelength of 0.90 m and a frequency of 120 Hz. Two points A and B lie along the direction of travel of the wave, 0.15 m apart.

   (a)

   What is the phase difference between the oscillations at A and B?

   [1 mark]

   • Aπ/3 rad
   • B12π rad
   • Cπ/6 rad
   • D2π/3 rad

   (b)

   Which statement gives the condition for two sources to be coherent?

   [1 mark]

   • AThey are in the same medium.
   • BThey have the same amplitude.
   • CThey are the same distance from the observer.
   • DThey have the same frequency and a constant phase difference.

   (c)

   Calculate the minimum separation of two points on the wave that are exactly in antiphase.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   Two identical dippers, S₁ and S₂, vibrate in phase at 8.0 Hz in a ripple tank, each producing circular waves of wavelength 2.5 cm. A point Q on the water surface is 20.0 cm from S₁ and 25.0 cm from S₂.

   (a)

   State what is meant by superposition, and explain why the dippers must be coherent to produce a stable interference pattern.

   [3 marks]

   (b)

   Calculate the path difference at Q, and hence deduce the type of interference at Q and the phase difference between the two waves there.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A teacher connects two loudspeakers in parallel to a single signal generator set to 850 Hz, so that they emit sound in phase. The speed of sound in the room is 340 m s⁻¹. A pupil walks along a line parallel to the line joining the speakers and hears the loudness alternate between loud and quiet. The teacher then asks why a similar pattern is not seen when two separate filament lamps are used instead.

   (a)

   Explain why the pupil hears alternate loud and quiet sounds, using the ideas of wavefronts, path difference and phase difference, and find the path difference at the first quiet position.

   [6 marks]

   (b)

   Explain why a similar interference pattern is not seen with two separate filament lamps, and why the loudspeakers can show it.

   [6 marks]

   Total for question 4: 12 marks

End of questions