Question 24: Waves

Question

A car is moving towards a high cliff. The car driver sounds a horn of frequency $$f$$. The reflected sound heard by the driver has a frequency $$2 f$$. If $$v$$ be the velocity of sound, then the velocity of the car in the same velocity units, will be

Accepted Answer

When the sound is reflected from the cliff, it approaches the driver of the car. Therefore, the driver, acts as an observer and both the source (car) and observer are moving.
Hence, apparent frequency heard by the observer (driver) is given by
$$f^{\prime}=f\left(\frac{v+v_o}{v-v_s}ight)\quad$$ .... (i)
where, $$\quad v_s=$$ velocity of sound
and $$\quad v_o=$$ velocity of the car
Thus, Eq. (i) becomes
$$\begin{aligned}
2 f & =f\left(\frac{v+v_o}{v-v_o}ight) \
\Rightarrow 2 v-2 v_o & =v+v_o \Rightarrow 3 v_o=v \Rightarrow v_o=\frac{v}{3}
\end{aligned}$$

Answer

$$\frac{v}{\sqrt{2}}$$

Answer

$$\frac{v}{3}$$

Answer

$$\frac{v}{4}$$

Answer

$$\frac{v}{2}$$

Waves

A car is moving towards a high cliff. The car driver sounds a horn of frequency $f. The reflected sound heard by the driver has a frequency 2 f. If v$ be the velocity of sound, then the velocity of the car in the same velocity units, will be

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