A loudspeaker oscillates with frequency f to produce sound waves of wavelength λ. The loudspeaker makes N oscillations in time t.

1. (a)(i)State expressions, in terms of some or all of the symbols f, λ and N, for: 1. the distance moved by a wavefront in time t 2. time t.[2]
2. (a)(ii)Use your answers in (i) to deduce the equation relating the speed v of the sound wave to f and λ.[1]
3. (b)The waveform of a sound wave is displayed on the screen of a cathode-ray oscilloscope (c.r.o.), as shown in Fig. 5.1. [Figure 5.1] The time-base setting is 0.20 ms cm⁻¹. Determine the frequency of the sound wave.[2]
4. (c)Two sources S₁ and S₂ of sound waves are positioned as shown in Fig. 5.2. [Figure 5.2] The sources emit coherent sound waves of wavelength 0.85 m. A sound detector is moved parallel to the line S₁S₂ from a point X to a point Y. Alternate positions of maximum loudness L and minimum loudness Q are detected, as illustrated in Fig. 5.2. Distance S₁X is equal to distance S₂X. Distance S₂Y is 7.40 m.
5. (c)(i)Explain what is meant by coherent waves.[1]
6. (c)(ii)State the phase difference between the two waves arriving at the position of minimum loudness Q that is closest to point X.[1]
7. (c)(iii)Determine the distance S₁Y.[2]

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