When both the listener and source are moving towards each other, then which of the following is true regarding frequency and wavelength of wave observed by the observer?

Question

When both the listener and source are moving towards each other, then which of the following is true regarding frequency and wavelength of wave observed by the observer? (A) More frequency, less wavelength (B) More frequency, more wavelength (C) Less frequency, less wavelength (D) More frequency, constant wavelength

Tardigrade Admin · Accepted Answer

According to Doppler's effect, whenever there is a 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 S be source of sound and L the listener of sound. Let v be the actual frequency of sound emitted by the source and

λ

be the actual wavelength of the sound emitted.
If v is velocity of sound in still air, then

λ = \frac{v}{V}

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

v^{''} = \frac{v - v _{L}}{v - s _{s}} \times V

Here, both source and listener are approaching each other.

Solution

Then

v_{s}

is positive and

v_{L}

is negative.

∴ v^{''} = \frac{v - ( - v _{L} )}{v - v _{s}} v = (\frac{v + v _{L}}{v - v _{s}}) v

i . e ., v^{''} > v

Also,

λ^{''} < λ

So, listener listens more frequency and observes less wavelength.

Then vs is positive and vL is negative. ∴ vâ² â²=(v - (- vL)/v - vs)v=((v + vL/v - vs))v i.e., vâ² â²>v Also, λ â² â² < λ So, listener listens more frequency and observes less wavelength.

Q. When both the listener and source are moving towards each other, then which of the following is true regarding frequency and wavelength of wave observed by the observer?

More frequency, less wavelength

More frequency, more wavelength

Less frequency, less wavelength

More frequency, constant wavelength