Progressive wavesAQA A-Level Physics: Subtopic test

1. 1
   A student uses a vibrating dipper to generate straight water waves in a ripple tank. The dipper vibrates at 12 Hz and the student measures the distance between adjacent wave crests on the water surface as 2.5 cm.

   (a)

   What is the period of the oscillation of a point on the water surface?

   [1 mark]

   • A12 s
   • B0.083 s
   • C0.025 s
   • D0.30 s

   (b)

   What is the speed of the water waves?

   [1 mark]

   • A4.8 m s⁻¹
   • B30 m s⁻¹
   • C2.1 × 10⁻³ m s⁻¹
   • D0.30 m s⁻¹

   (c)

   The student doubles the frequency of the dipper. The speed of the waves is unchanged because the depth of water is unchanged. Calculate the new wavelength.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   Two buoys, A and B, float on a lake in line with the direction in which a sinusoidal water wave is travelling. The wave has frequency 0.50 Hz and wavelength 8.0 m. Buoy B is 3.0 m further along the direction of travel than buoy A.

   (a)

   What is the speed of the wave?

   [1 mark]

   • A4.0 m s⁻¹
   • B16 m s⁻¹
   • C0.063 m s⁻¹
   • D8.5 m s⁻¹

   (b)

   What is the phase difference between the motion of buoy A and the motion of buoy B?

   [1 mark]

   • A0.38 rad
   • B1.2 rad
   • C2.4 rad
   • D4.7 rad

   (c)

   Calculate the time by which the motion of buoy B lags behind that of buoy A.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A loudspeaker produces a continuous pure note of frequency 850 Hz in air, where the speed of sound is 340 m s⁻¹. Two small microphones are placed in a straight line with the loudspeaker, at distances of 1.20 m and 1.50 m from it.

   (a)

   Calculate the wavelength of the sound and the phase difference, in radians, between the signals at the two microphones.

   [3 marks]

   (b)

   The microphone that is further from the loudspeaker is moved slowly directly away from it. Determine the distance it must move before the two signals are next in phase, and explain your answer.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A long rope is stretched horizontally. One end is attached to an oscillator that moves it up and down sinusoidally with frequency 4.0 Hz and amplitude 0.030 m, producing a progressive wave that travels along the rope at 2.4 m s⁻¹. Energy losses along the rope are negligible.

   (a)

   Describe the motion of a single point on the rope, and explain how the motion of a point 0.15 m further from the oscillator compares with it. Include calculations of the wavelength and the phase difference in your answer.

   [6 marks]

   (b)

   The frequency of the oscillator is doubled to 8.0 Hz, with the amplitude unchanged. A student claims that the wave on the rope now travels twice as fast. Evaluate the student's claim, and calculate the new wavelength and the new phase difference between two points 0.15 m apart.

   [6 marks]

   Total for question 4: 12 marks

End of questions