1. 1
   A guitar string is fixed at both ends, with a vibrating length of 0.65 m. When plucked it vibrates in its first harmonic (fundamental) at a frequency of 110 Hz.

   (a)

   What is the wavelength of the wave on the string in the first harmonic?

   [1 mark]

   • A0.33 m
   • B0.65 m
   • C2.60 m
   • D1.30 m

   (b)

   Two points on the string are 0.20 m and 0.45 m from one end. What is the phase difference between their oscillations in the first harmonic?

   [1 mark]

   • Aπ/2 rad
   • Bπ rad
   • C0
   • DIt varies with time

   (c)

   The string is made to vibrate in its third harmonic. Calculate the frequency and the distance between adjacent nodes.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   Two organ pipes are each 0.85 m long. Pipe X is open at both ends and pipe Y is closed at one end. The speed of sound in the air in the pipes is 340 m s⁻¹. A microphone near the pipes records a note that contains frequencies of 600 Hz and 1000 Hz and comes from only one of the pipes.

   (a)

   What is the frequency of the first harmonic of pipe Y?

   [1 mark]

   • A50 Hz
   • B100 Hz
   • C200 Hz
   • D400 Hz

   (b)

   Which frequency can NOT be produced by pipe Y?

   [1 mark]

   • A400 Hz
   • B100 Hz
   • C300 Hz
   • D500 Hz

   (c)

   Deduce which pipe produced the recorded note.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A mass hanging on a spring is driven up and down by a vibration generator whose frequency can be varied. A student records the steady amplitude of the mass at each driving frequency: 1.0 Hz, 0.8 cm; 1.5 Hz, 1.6 cm; 1.8 Hz, 4.0 cm; 2.0 Hz, 9.5 cm; 2.2 Hz, 3.8 cm; 2.5 Hz, 1.4 cm; 3.0 Hz, 0.7 cm. She then attaches a large, light card to the mass and repeats the experiment. The largest amplitude is now 3.1 cm, at 1.95 Hz, while the amplitudes at 1.0 Hz and 3.0 Hz are almost unchanged.

   (a)

   Identify the natural frequency of the system and explain why the amplitude is largest at this driving frequency.

   [3 marks]

   (b)

   Compare the two sets of results and explain the effect of attaching the card.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A microwave transmitter faces a flat metal plate 60 cm away. A small detector is moved slowly along the line between them. Close to the plate, the detector reading rises and falls between strong maxima and minima that are almost zero. The minima are 1.4 cm apart. Close to the transmitter the minima are still 1.4 cm apart, but the readings at the minima are much larger and the pattern is less distinct.

   (a)

   Explain how the pattern of maxima and minima is formed, and determine the frequency of the microwaves.

   [6 marks]

   (b)

   Contrast the standing wave between the transmitter and the plate with the travelling wave emitted by the transmitter, and explain why the minima near the transmitter are less distinct.

   [6 marks]

   Total for question 4: 12 marks

End of questions