Q.

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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a

740 Hz, 800 Hz

b

800 Hz, 750 Hz

c

 800 Hz, 880 Hz

d

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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