Wave properties and wave graphsEdexcel A-Level Physics: Subtopic test

1. 1
   A student displays the signal from a microphone on an oscilloscope. The time base is set to 0.50 ms per division and the Y-gain to 2.0 V per division. One complete cycle of the trace spans 4.0 divisions horizontally, and the distance from a trough to the next crest spans 5.0 divisions vertically. The speed of sound in air is 340 m s⁻¹.

   (a)

   What is the frequency of the signal?

   [1 mark]

   • A2000 Hz
   • B125 Hz
   • C500 Hz
   • D0.50 Hz

   (b)

   What is the amplitude of the signal?

   [1 mark]

   • A10 V
   • B5.0 V
   • C2.5 V
   • D20 V

   (c)

   Calculate the wavelength of the sound wave.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A technician sends a sound wave along a long air-filled tube using a loudspeaker. She is interested in how the pressure of the air and the displacement of the air molecules from their equilibrium positions vary as a progressive wave passes along the tube.

   (a)

   Which statement about the motion of the air molecules is correct?

   [1 mark]

   • AThey oscillate perpendicular to the direction of energy transfer.
   • BThey travel steadily along the tube at the wave speed.
   • CThey oscillate in a circle in the plane of the tube.
   • DThey oscillate parallel to the direction of energy transfer about fixed equilibrium positions.

   (b)

   At a point where the pressure is at its maximum in a progressive wave, what is the displacement of the air molecules from their equilibrium positions?

   [1 mark]

   • AZero, because molecules on both sides are displaced towards this point
   • BMaximum, in the direction of travel of the wave
   • CMaximum, opposite to the direction of travel of the wave
   • DEqual to one wavelength

   (c)

   Explain how the wave transfers energy along the tube although there is no net movement of air along it.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A student determines the speed of sound in air. A loudspeaker driven by a signal generator at 2000 Hz is placed at one end of a metre rule. Two microphones are connected to the two channels of an oscilloscope. Microphone 1 stays next to the loudspeaker and microphone 2 is moved slowly along the rule. The student records each position of microphone 2 at which the two traces are exactly in phase. The distance between the first and the sixth in-phase positions is 0.850 m.

   (a)

   Calculate the speed of sound in air from the student's results.

   [3 marks]

   (b)

   Explain why the student measures the distance over five wavelengths rather than one, and describe how measurements at several frequencies could be used to find a more reliable value for the speed of sound.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A teacher uses a stretched cord, fixed at both ends 2.4 m apart, and a long soft spring to demonstrate waves. A vibration generator sends transverse waves along the cord and she pushes and pulls the end of the spring to send longitudinal waves along it. A data logger records the displacement of single points, and the students also sketch displacement against distance for the whole of each medium at one instant.

   (a)

   Compare transverse waves on the cord with longitudinal waves on the spring, and explain what the displacement–distance graph and the displacement–time graph show for these waves and how they are linked.

   [6 marks]

   (b)

   The generator is set to 15 Hz and the cord shows a stationary wave with exactly two loops between the fixed ends. The maximum amplitude at the antinodes is 1.5 cm. Determine the speed of the progressive waves that make up the stationary wave. Then compare the displacement–time graphs for a point at an antinode and for a point in the same loop 0.30 m from the nearest node, giving numerical values where you can.

   [6 marks]

   Total for question 4: 12 marks

End of questions