A police car with a siren of frequency $8 \mathrm{kHz}$ is moving with uniform velocity $36 \mathrm{~km} /…

A police car with a siren of frequency $8 \mathrm{kHz}$ is moving with uniform velocity $36 \mathrm{~km} / \mathrm{h}$ towards a tall building which reflects the sound waves. The speed of sound in air is $320 \mathrm{~m} / \mathrm{s}$. The frequency of the siren heard by the car driver is
  1. $8.50 \mathrm{kHz}$
  2. $8.25 \mathrm{kHz}$
  3. $7.75 \mathrm{kHz}$
  4. $7.50 \mathrm{kHz}$

Solution


Apparent frequency of sound heard by car driver (observer) reflected from the building will be $ \begin{aligned} f^{\prime} & =f\left(\frac{v+v_0}{v-v_s}\right) \\ & =8\left(\frac{320+10}{320-10}\right) \\ & =8.5 \mathrm{kHz} \end{aligned} $ $\therefore$ Correct option is (a). Analysis of Question (i) Question is simple. (ii) Driver will listen two sounds, direct and reflected. Direct sound will be of $8 \mathrm{kHz}$ as driver has no relative motion with the car. But reflected sound is of increased frequency because driver and image of car both are approaching towards each other

Asked in: JEE Advanced 2011 (Paper 1)

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