Question

A racing car moving towards a cliff sounds its horn. The sound reflected from the cliff has a pitch one octave higher than the actual sound of the horn. If V is the velocity of sound, the velocity of the car is ______.

विकल्प

• `V/sqrt2`

• `V/2`

• `V/3`

• `V/4`

Answer 1

A racing car moving towards a cliff sounds its horn. The sound reflected from the cliff has a pitch one octave higher than the actual sound of the horn. If V is the velocity of sound, the velocity of the car is `bbunderline(V/2)`.

Explanation:

Let velocity of car be u,

`v_{direct} = v_S`

The cliff behaves as a observer which  receives sound of frequency `(V/(V - u))ν` from approaching source.

The cliff then acts as a source of same frequency which it receives i.e. `(V/(V - u))ν`.

The car then behaves as a observer, approaching source of frequency `(V/(V - u))ν`.

So, frequency of sound reflected from cliff,

= `(V/(V - u))ν`

= `(V/(V - u))ν = 2ν`

Now, V = 2V - 2u

Or, u = `V/2`