Progressive and stationary wavesAQA A-Level Physics: Topic test

1. 1
   A tuning fork of frequency 512 Hz emits sound into air, where the speed of sound is 340 m s⁻¹.

   (a)

   What is the wavelength of the sound?

   [1 mark]

   • A1.5 m
   • B0.66 m
   • C1.7×10⁵ m
   • D1.9×10⁻³ m

   (b)

   What is the phase difference between the vibrations of air particles at two points 0.166 m apart along the direction of travel of the sound?

   [1 mark]

   • Aπ/4 rad
   • Bπ rad
   • C0.25 rad
   • Dπ/2 rad

   (c)

   Calculate the period of the sound wave and the time taken for the phase of the vibration of the air at a fixed point to change by π rad.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   Earthquakes produce P-waves, which are longitudinal, and S-waves, which are transverse. A seismic station is 3600 km from the epicentre of an earthquake. The P-waves travel at 8.0 km s⁻¹ and the S-waves travel at 4.5 km s⁻¹ through the rock.

   (a)

   Which statement about the P-waves is correct?

   [1 mark]

   • AThe particles of rock oscillate parallel to the direction in which the energy is transferred.
   • BThe particles of rock oscillate perpendicular to the direction in which the energy is transferred.
   • CThe waves can be plane polarised.
   • DThe waves are electromagnetic waves.

   (b)

   Which of the following can be plane polarised?

   [1 mark]

   • AThe P-waves
   • BSound waves in air
   • CThe S-waves
   • DLongitudinal waves on a coiled spring

   (c)

   Calculate how much later the S-waves arrive at the station than the P-waves.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A stretched string of length 0.80 m is fixed at both ends and vibrates in its third harmonic at a frequency of 330 Hz. The mass per unit length of the string is 3.5×10⁻³ kg m⁻¹.

   (a)

   Calculate the wavelength of the stationary wave and the speed of waves on the string.

   [3 marks]

   (b)

   Calculate the tension in the string. The tension is then increased by 21%. Calculate the new frequency of the first harmonic.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A loudspeaker at one end of a horizontal glass tube produces sound of frequency 680 Hz. A flat plate at the other end reflects the sound and a stationary wave forms in the air in the tube. Fine powder sprinkled along the tube collects in small heaps at points that are 0.25 m apart.

   (a)

   Explain how the stationary wave forms and why the powder collects in heaps. Calculate the speed of sound in the tube.

   [6 marks]

   (b)

   Compare this stationary wave with a progressive sound wave of the same frequency in terms of amplitude, phase and energy transfer. Explain the phase relationship between air particles on opposite sides of a node, and calculate the distance from a node to the nearest antinode.

   [6 marks]

   Total for question 4: 12 marks

5. 5
   A bridge cable of length 40 m is fixed at both ends and is set vibrating by the wind in its second harmonic at a frequency of 1.5 Hz. The mass per unit length of the cable is 25 kg m⁻¹.

   (a)

   How many nodes are there along the cable, including the two at the ends?

   [1 mark]

   • A2
   • B4
   • C1
   • D3

   (b)

   What is the speed of transverse waves on the cable?

   [1 mark]

   • A30 m s⁻¹
   • B60 m s⁻¹
   • C120 m s⁻¹
   • D0.04 m s⁻¹

   (c)

   Calculate the tension in the cable.

   [2 marks]

   Total for question 5: 4 marks

6. 6
   A photographer fits a polarising filter to a camera to reduce glare from the surface of a lake. The light reflected from the water is partly plane polarised, with its oscillations in the horizontal plane.

   (a)

   How should the transmission axis of the filter be orientated to reduce the glare most?

   [1 mark]

   • AHorizontal
   • BAt 45° to the horizontal
   • CVertical
   • DThe orientation does not matter.

   (b)

   A fully plane-polarised beam is viewed through a polarising filter that is rotated through 360° about the line of sight. How many times does the transmitted brightness fall to zero?

   [1 mark]

   • A2
   • B1
   • C4
   • D0

   (c)

   Explain why the fact that light can be plane polarised shows that light is a transverse wave.

   [2 marks]

   Total for question 6: 4 marks

7. 7
   Ultrasound of frequency 3.5 MHz is used in a medical scanner. The speed of ultrasound in soft tissue is 1540 m s⁻¹.

   (a)

   Calculate the wavelength of the ultrasound in the tissue and the phase difference, in radians, between the vibrations of two points in the tissue that are 0.11 mm apart along the direction of travel.

   [3 marks]

   (b)

   A pulse of ultrasound is reflected from a boundary in the tissue and the echo returns to the scanner after 1.04×10⁻⁴ s. Calculate the depth of the boundary. Explain whether ultrasound can be plane polarised.

   [4 marks]

   Total for question 7: 7 marks

8. 8
   A teacher demonstrates properties of microwaves. A transmitter emits vertically plane-polarised microwaves of frequency 10.5 GHz towards a receiver. In demonstration A, a grille made of parallel metal rods is placed between the transmitter and the receiver and is rotated in its own plane through 360°. In demonstration B, the grille is removed, a flat metal sheet reflects the microwaves back towards the transmitter, and the receiver probe is moved along the line between the transmitter and the sheet. Use c = 3.00×10⁸ m s⁻¹.

   (a)

   In demonstration A, describe and explain what happens to the signal at the receiver as the grille is rotated through 360°, and explain what this shows about microwaves.

   [6 marks]

   (b)

   In demonstration B, the receiver probe detects a series of minima and maxima. Calculate the wavelength of the microwaves and the distance between adjacent minima. Explain how the stationary wave is formed and why the minima do not reach exactly zero in practice.

   [6 marks]

   Total for question 8: 12 marks

End of questions