Doppler Effect Wind: Frequency, Velocity, Wavelength

[sachin123]

Homework Statement

An observer is in rest.A source of sound is in rest.A wind blows along the line joining the observer and the source.What all remain same in these:
a.frequency b.velocity of sound c.wavelength

Homework Equations

f prime=f(v+w-vo)/(v+w-vs)
Doppler effect

The Attempt at a Solution

frequency has to remain same since there is no relative motion.
v should remain same because wind cannot influence speed of sound.
wavelength has to obviously remain the same (from the above).
But my book says only frequency remains same.
Please explain.

 

[Stonebridge]

The confusion is over the meaning of "speed of sound" here.
The question means as measured relative to the ground, rather than speed in still air.
In this case the speed increases by an amount equal to the wind speed, and the wavelength is made proportionally larger.
f=speed / wavelength
both speed and wavelength increase. (Such that f stays the same.)

 

[sachin123]

You:In this case the speed increases by an amount equal to the wind speed.


So speed of sound with respect to the ground is 400 m/s when wind velocity is 70 m/s?
Can we add velocity of sound and wind vectorially?

 

[Stonebridge]

You:In this case the speed increases by an amount equal to the wind speed.


So speed of sound with respect to the ground is 400 m/s when wind velocity is 70 m/s?
Can we add velocity of sound and wind vectorially?

Yes if the speed was 330m/s in still air and we measure the speed in the same direction as the wind blows.
Yes, the velocities are added vectorially.