If a listener L is at rest and the siren in previous illustrantion is moving away from L at a speed of `30(m)/(s)`, what frequency does the listener hear?

Explanation

Our target variable is the frequency `f_I`. Heard by the listener, who is behind the moving source Figure. Shows the situation. We know that `v_i=0` and `v_s=30(m)/(s)` (The source velocity `v_S` is positive because the siren is moving in the same direction as the direction from listener to source.)
`f_I=(v)/(v+v_S)f_S=(340(m)/(s))/(340(m)/(s)+30(m)/(s))(300Hz)=276Hz`
The source and listener are moving apart, so the frequency `f_I` heard by the listener is less than the frequency `f_S` emitted by the source.
Here is an alternative approach we can use to chack our result. From previous illustration the wavelength behind the source (which is where the listener in figure is located) is `1.23m`, so
`f_L=(v)/(lamda)=(340(m)/(s))/(1.23m)=276m`
Even though the source is moving, the wave speed v relative to the stationary listener is unchanged.