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A train running at 108 km/hr towards east whistles at a frequency of 800 Hz. The frequencies heard by a passenger sitting in the train and a person standing near the track whom the train has just passed (Speed of Sound =330 m/s)

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740 Hz, 800 Hz

800 Hz, 750 Hz

800 Hz, 880 Hz

800 Hz, 733 Hz

answer is A.

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Detailed Solution

With respect to passenger sitting in the train, there is no relative motion.

$\large \therefore$ n^' = n = 800Hz

Velocity of the source = $\large 108 \times \frac{5}{{18}}m/s$

= 30 m/s

With respect to person standing near the track whom the train has just passed.

$\large n\, = \,n\left( {\frac{v}{{v + {v_s}}}} \right)\,\, \Rightarrow \, = \,800\left( {\frac{{330}}{{330 + 30}}} \right)$

= $\large 800 \times \frac{{330}}{{360}}\, \Rightarrow \, = \,733\,Hz$

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