Question

a siren emitting a note of frequency n is fitted on a police van, traveling towards a stationary listener. What is the velocity of the van, if the frequency of the note heard by the listener is double the original frequency?
a) Vs = V
b) Vs=V/2
c) Vs = 2V
d) Vs=V/3

Answer 1

Answer on Question #64002 – Physics – Mechanics | Relativity

Question:

A siren emitting a note of frequency $n$ is fitted on a police van, traveling towards a stationary listener. What is the velocity of the van, if the frequency of the note heard by the listener is double the original frequency?

a) $V_s = V$

b) $V_s = V / 2$

c) $V_s = 2V$

d) $V_s = V / 3$

Answer:

Here's an equation for Doppler Effect:

$$\nu = \nu_0 \frac{V + V_l}{V - V_s};$$

In this situation $V_l = 0$:

$$\nu = \nu_0 \frac{V}{V - V_s} \Rightarrow 2\nu_0 = \nu_0 \frac{V}{V - V_s} \Rightarrow 2 = \frac{V}{V - V_s} \Rightarrow 2V - 2V_s = V \Rightarrow V = 2V_s \Rightarrow V_s = \frac{V}{2}.$$

So, answer is b) $V_s = V / 2$.

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