A horizontal string is stretched between two fixed points X and Y. A vibrator is used to oscillate the string and produce a stationary wave. Fig. 4.2 shows the string at one instant in time. The speed of a progressive wave along the string is 30ms⁻¹. The stationary wave has a period of 40 ms. A particle on the string oscillates with an amplitude of 13mm. At time t, the particle has zero displacement.

1. (a)On Fig. 4.1, complete the two graphs to illustrate what is meant by the amplitude A, the wavelength λ and the period T of a progressive wave. [Figure 4.1] Ensure that you label the axes of each graph.[3]
2. (b)(i)Explain how the stationary wave is formed on the string.[2]
3. (b)(ii)1.Calculate 1. the displacement of the particle at time (t + 100ms), displacement = ..................................................... mm[3]
4. (b)(ii)2.2. the total distance moved by the particle from time t to time (t + 100ms). distance = ..................................................... mm[3]
5. (b)(iii)1.Determine 1. the frequency of the wave, frequency = ..................................................... Hz[1]
6. (b)(iii)2.2. the horizontal distance from X to Y. distance = ..................................................... m[3]

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