Question

Two engines cross each other travelling in opposite directions at 108km/hr. One engine sounds a whistle of frequency 540Hz. What is the frequency of sound heard by the other engine before they cross each other? Does the frequency of sound heard by the other engine remain same after crossing? Take speed of sound 330m/s.

Solution

Before crossing, both the engines are approaching each other.
Thus, the apparent frequency of sound is,

straight v subscript 1 equals fraction numerator straight V plus straight u subscript straight o over denominator straight V minus straight u subscript straight s end fraction straight v

Here,

straight V equals 330 space straight m divided by straight s

straight u subscript straight o equals straight u subscript straight s equals 108 space km divided by hr space equals space 30 space straight m divided by straight s space straight v space equals space 540 space Hz

∴ Apparent frequency,

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After crossing, both the engines are moving away from each other.
Thus, the apparent frequency of sound is,

straight v subscript 1 equals fraction numerator straight V minus straight u subscript straight o over denominator straight V plus straight u subscript straight s end fraction straight v

∴

space space space space straight v subscript 1 equals fraction numerator 330 minus 30 over denominator 330 plus 30 end fraction cross times 540 equals 450 Hz

The frequency of sound heard by the other engine changes after crossing.

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