Question

Suppose you are stopped for a traffic light, and an ambulance approaches you from behind with a speed of 18.5 m/s. The siren on the ambulance produces sound with a frequency of 959 Hz as measured when you are at rest relative to the ambulance. The speed of sound in air is 343 m/s. What is the wavelength of the sound reaching your ears?

Answer 1

using dopplers equation.....

we can use a simplified one for just the source moving,

f_new = f_old [ 1 / ( 1- ( u/v ))]

where u is the speed of the source, v is the speed of sound in air, and we use a minus sign because it is approaching towards us ( instead of traveling away from us, where we would use a plus in the denominator ).

f_new = 959 Hz [ 1 / ( 1- ( 18.5 / 343 ))]

fnew = 1013.67 Hz.

Now, we use v = λf to find the wavelength

343 m/s = λ( 1013.67 Hz )

λ = .3383 m