Doppler Effect + Wavelength problem

[KendrickLamar]

Homework Statement

A sound source emits sounds of frequency 210 Hz that travel through still air at 340 m/s. The listener moves at 85 m/s relative to still air toward the stationary source. What is the wavelength of the sound between the source and the listener?

Homework Equations

f' = f[1+ Vlistener/Vsound]
v=(wavelength)f

The Attempt at a Solution

well using the doppler effect since the listener is moving towards the stationary source i know it will be f'=f[1+Vlistener/Vsound]

i find the f' right... but when using v=wavelength*frequency, which frequency do i actually use. because i know although I am solving for f' , I am just wondering if its a trick or something because I'm a little confused on the concept.

so for f' i get 262.5 Hz

then i plug it into the v=wavelength*freq , but which velocity do i use? the speed of sound or the speed of the listener moving?

using the speed of sound i get 340 m/s = wavelength * 262.5 and end up with 1.295m as the wavelength.

 

[Stonebridge]

If the source is not moving the waves are unchanged and their wavelength is simply given by v/f where v is their speed in still air and f the original frequency.
The frequency of the sound heard by the moving listener is higher because he passes through the approaching waves at a higher rate than if he were stationary. The Doppler formula will give this new frequency.