Physics - Sound Wave Question with Solution | TestHub

According to Doppler's effect, whenever there is relative motion between a source of sound and listener, the apparent frequency of sound heard by the listener is different from the actual frequency of sound emitted by the source. Let$\mathrm{S}$be source of sound and$\mathrm{L}$the listener of sound. Let$\nu$be the actual frequency of sound emitted by the source and$\lambda$be the actual wavelength of the sound emitted.

If$v$is velocity of sound in still air, then
$\lambda =\frac{v}{\nu }$
If velocity of listener is$v_L$and velocity of source is$v_s$, then apparent frequency of sound waves heard by the listener is
$\nu \text{'}=\frac{v-v_L}{v-s_s}\times \nu$
Here, both source and listener are approaching each other.

Then$v_s$is positive and$v_L$is negative.
$\therefore \nu \text{'}=\frac{v-\left(-v_L\right)}{v-v_s}\times \nu =\left(\frac{v+v_L}{v-v_s}\right)\nu$
$\Rightarrow \nu \text{'}>\nu$
Also,$\lambda \text{'}<\lambda$
So, listener listens more frequency and observes less wavelength.