Physics 9702 · AS & A Level · Progressive waves

Progressive waves — practice question

A progressive longitudinal wave moves through a medium from left to right. Fig. 4.1 gives the positions of some of the medium’s particles at time $t_0$ and also a graph of the particle displacements at that same time $t_0$. On the graph, displacements to the right of equilibrium are shown as positive and displacements to the left as negative. The period of the wave is $T$.
(a(i))[1]

On Fig. 4.1, circle two particles that are exactly one wavelength apart.

(a(ii))[3]

On Fig. 4.1, sketch a line on the graph to show the particle displacements for the longitudinal wave at time $t_0 + \frac{T}{4}$.

(a(iii))[1]

State the direction in which particle $Z$ is moving at time $t_0 + \frac{T}{4}$.

(b)[3]

The frequency of the wave in (a) is $16\,\text{kHz}$. The separation between particles $X$ and $Y$ is $0.19\,\text{m}$. Calculate the speed at which the wave moves through the medium.

(c)[2]

A longitudinal sound wave is travelling through a solid. Its initial intensity is $I_0$. The frequency stays constant and the amplitude drops to half of its original value. Determine the final intensity of the wave in terms of $I_0$.

(d(i))[1]

The sound wave in (c) now meets a second sound wave moving in the opposite direction. State one condition needed for these two waves to form a stationary wave.

(d(ii))[2]

State two differences between a stationary wave and a progressive wave.

Worked solution & mark scheme

This 13-mark question has a full step-by-step worked solution and mark scheme. One marking point: Two particles correctly identified with seven particles between them

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