A1. This question is about standing (stationary) waves.

(a) Describe two ways that standing waves are different from travelling waves.

(b) An experiment is carried out to measure the speed of sound in air, using the apparatus shown below.

A tube that is open at both ends is placed vertically in a tank of water, until the top of the tube is just at the surface of the water. A tuning fork of frequency 440 Hz is sounded above the tube. The tube is slowly raised out of the water until the loudness of the sound reaches a maximum for the first time, due to the formation of a standing wave.

(i) Explain the formation of a standing wave in the tube.

(ii) State the position in the tube that is always a node.

(iii) The tube is raised a little further. Explain why the loudness of the sound is no longer at a maximum.

(c) The tube is raised until the loudness of the sound reaches a maximum for a second time.Between the two positions of maximum loudness, the tube has been raised by 36.8 cm.The frequency of the sound is 440 Hz. Estimate the speed of sound in air.


A2. This question is about the Doppler effect.

The sound emitted by a car’s horn has frequency f , as measured by the driver. An observer moves towards the stationary car at constant speed and measures the frequency of the sound to be f'.

(a) Explain, using a diagram, any difference between f'and f.

(b) The frequency f is 3.00×102Hz. An observer moves towards the stationary car at a constant speed of 15.0ms−1. Calculate the observed frequency f'. of the sound. The speed of sound in air is 3.30×102ms−1.


A3. This question is about optical resolution and accommodation.

A woman is walking along a straight path, which is at right angles to a telephone line, as shown in the diagram below. Two birds are perched on the line, 0.40 m apart.

The diameter of the pupil of the woman’s eye is 2.5 mm and the average wavelength of visible light is 550 nm.

(a) Use the Rayleigh criterion to estimate the distance D at which the woman will just be able to see two separate birds.

(b) The woman looks down at her watch and is able to focus on it clearly. Explain how her eyes are able to focus on near objects as well as far objects.




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