How Does Observer Velocity Affect Sound Wavefront Frequency?

[Tanero]

Homework Statement

A source of sound emits waves at a frequency f 450 Hz. An observer is located at a distance d 150 m from the source. If the observer is moving away from the source at a velocity v_obs 40 m/s, how does the number of wavefronts change with time? dN/dt ? (in Hz)

Homework Equations

λ=u/f
N=d/λ
u - speed of sound

The Attempt at a Solution

with moving observer my frequency changes. f'=(u/u+v_obs)*f_source
λ'=u/(u/u+v_obs)*f_source)=(u+v_obs)/f

in time Δt, ΔN=(d+v_obsΔt)/λ' - d/λ'

then I find a limit for Δt>0 lim ΔN/Δt= dN/dt

Am I on the right way?

 

[Simon Bridge]

1 wavefront arrives per cycle.
The number of wavefronts that arrive per unit time is the number of cycles per second - what quantity is measured in cycles per second?

 

[Tanero]

1 wavefront arrives per cycle.
The number of wavefronts that arrive per unit time is the number of cycles per second - what quantity is measured in cycles per second?

Just frequency? No need of all that ΔN/Δt calcs?

Then, if observer is receding f' = u/[(u+v_obs)*f_source]
Is it? dN/dt = f' . Is that what you mean?

 

[Simon Bridge]

The number of wavefronts observed per second is the frequency of the sound observed :)

It's an odd way of asking for it though - and what does the distance to the source have to do with it?
It sounds to me like there may be some information missing from the problem statement.
Like if the observer was originally stationary and at t=0 suddenly starts moving ... then the frequency would change with time.

 

[HalfLostAndSearching]

Yes, you are on the right track. The Doppler effect is definitely a factor in this scenario. However, there are a few other things to consider as well. First, you need to calculate the wavelength of the sound waves using the given frequency and the speed of sound. Then, you can use the formula N=d/λ to calculate the number of wavefronts at the starting point.

Next, you need to take into account the observer's velocity and its effect on the wavelength. As the observer moves away from the source, the wavelength will increase due to the Doppler effect. This means that the number of wavefronts will decrease over time.

To calculate the change in the number of wavefronts, you can use the formula ΔN=(d+vobsΔt)/λ' - d/λ, where λ' is the new wavelength with the observer's velocity taken into account.

Then, to find the rate of change of the number of wavefronts with time, you can take the limit as Δt approaches 0. This will give you the instantaneous rate of change, or dN/dt.

Overall, your approach is correct, but make sure to take into account all the variables and use the appropriate formulas.