Physics 9702 · AS & A Level · Doppler effect for sound waves

Doppler effect for sound waves — practice question

The dolphin is moving underwater at a steady speed of $4.50\,\text{m s}^{-1}$.
(a)[2]

A dolphin sends out a sound while heading straight towards a stationary diver underwater. The diver hears the sound at $9560\,\text{Hz}$. The speed of sound in water is $1510\,\text{m s}^{-1}$. Find, to three significant figures, the frequency emitted by the dolphin.

(b)

The dolphin pushes on the bottom of a floating ball so that the ball moves straight upward from the water surface, as shown in Fig. 2.1. It leaves the surface with speed $5.6\,\text{m s}^{-1}$. Ignore air resistance.

(b(i))[2]

Calculate the greatest height reached by the ball above the water surface.

(b(ii))[1]

The ball leaves the water at $t = 0$ and reaches its greatest height at $t = T$. On Fig. 2.2, sketch how the ball’s speed varies with time $t$ from $t = 0$ to $t = T$. No numerical values are needed.

(b(iii))[2]

The mass of the ball is $0.45\,\text{kg}$. Using your value from (b)(i), calculate the change in gravitational potential energy of the ball as it rises from the water surface to its highest point.

(b(iv))[2]

State and explain how the magnitude of the ball’s acceleration changes as it returns towards the water surface if air resistance cannot be ignored.

Worked solution & mark scheme

This 9-mark question has a full step-by-step worked solution and mark scheme. One marking point: Substitute into $f_o = f_s \dfrac{v}{(v - v_s)} = 9560 \times \dfrac{1510}{(1510 - 4.50)}$.

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