One person moves towards a stationary source of sound with a speed `(1)/(5)` times the speed of sound. Sound emitted from the source has wavelength `lamda` and frequency f. Frequency and wavelength of sound heard by this person are respectively ......

Options

A. `0.8f,0.8 lamda`
B. `1.2 f, 1.2 lamda`
C. `1.2 f, lamda`
D. `f, 1.2 lamda`

Answer

C

Explanation

We have, `(f _(L))/( v + v _(L)) = (f _(S))/( v + v _(S))`
`therefore (f _(L))/( v + (v)/(5)) = (f _(S))/( jv + 0)`
`therefore (f_(L))/( (6v)/( 5)) = (f)/(v)`
`therefore f _(L) = (6)/(5) f = 1.2 f`
Here, velocity of sound wave w.r.t. listener is,
`v = v _(L) = v + (v)/(5) = (6v)/(5) = 1.2v`
Frequency of sound wave heard by listener is,
`f _(L) 1.2f`
Now, if wavelength of sound wave heard by the person is `lamda _(L)` then,
`v = v _(L) = f _(L) lamda _(L)`
`thereforef 1.2 v = 1.2 f xx lamda _(L)`
`therefore lamda _(L) = (v)/(f)`
`therefore lamda _(L) = lamda " "(because v = f lamda)`