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A train standing at the outer signal of a railway station blows a whistle of frequency $400 \mathrm{~Hz}$ still air. The train begins to move with a speed of $10 \mathrm{~ms}^{-1}$ towards the platform. What is the frequency of the sound for an observer standing on the platform? (sound velocity in air $=330 \mathrm{~ms}^{-1}$ )
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When the source (train) is moving towards the observer (platform) hence apparent frequency.
As given that,
frequency of whistle is, $v_0=400 \mathrm{~Hz}$
speed of train $\left(v_t\right)$ is, $v_t=10 \mathrm{~m} / \mathrm{s}$
velocity of sound in air $\left(v_a\right)$ is, $v_a=330 \mathrm{~m} / \mathrm{s}$
Apparent frequency by observer standing on platform when source is moving,
$$
\begin{aligned}
&v_{\text {app }}=\left(\frac{v_a}{v_a-v_t}\right) v_0=\left(\frac{330}{330-10}\right) 400 \\
&v_{\text {app }}=\frac{330}{320} \times 400=\frac{825}{2}=412.5 \mathrm{~Hz}
\end{aligned}
$$
As given that,
frequency of whistle is, $v_0=400 \mathrm{~Hz}$
speed of train $\left(v_t\right)$ is, $v_t=10 \mathrm{~m} / \mathrm{s}$
velocity of sound in air $\left(v_a\right)$ is, $v_a=330 \mathrm{~m} / \mathrm{s}$
Apparent frequency by observer standing on platform when source is moving,
$$
\begin{aligned}
&v_{\text {app }}=\left(\frac{v_a}{v_a-v_t}\right) v_0=\left(\frac{330}{330-10}\right) 400 \\
&v_{\text {app }}=\frac{330}{320} \times 400=\frac{825}{2}=412.5 \mathrm{~Hz}
\end{aligned}
$$
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