Frequency of two objects moving toward eachother

[eagles12]

Homework Statement

A motorcyclist and a police car are moving toward one another. The police car emits a sound with frequency of 502 Hz and has a speed of 27m/s. The motorcycle has a speed of 12 m/s.
What frequency does the motorcyclist hear?

Homework Equations

f=1/T
f'=f(1+v/vs)

The Attempt at a Solution

f'=502(1+27/12)
This gave me f'=1631.5 but it says this is incorrect

 

[MrWarlock616]

I think your equations are wrong. According to the Doppler Effect, the apparent frequency ##n_a=(\frac{V+V_o}{V-V_s}) n##

## V ## is the velocity of sound.

 

[eagles12]

so it would be
(27+343)/(12-343)*502
f=-561.15

 

[MrWarlock616]

read my post again.

 

[asteriatic]

.

I would first check to see if all the given variables and equations are correct and applicable to the situation. In this case, the equation used may not be the most appropriate for calculating the frequency heard by the motorcyclist. The equation f'=f(1+v/vs) is typically used for calculating the frequency shift due to the Doppler effect, but in this situation, the motorcyclist is not moving directly towards or away from the source of the sound (the police car).

Instead, we can use the formula v=fλ, where v is the speed of sound, f is the frequency, and λ is the wavelength. Since the speed of sound is constant, we can set up an equation using the given frequencies and speeds:

v=502λ
v'=fλ
where v' is the speed of sound heard by the motorcyclist.

We can then solve for f':

f'=(v'/λ)=(v/λ)*(v'/v)=(502/27)*(12/27)
This gives us a frequency of f'=237.9 Hz, which is the frequency that the motorcyclist would hear.

In conclusion, as a scientist, I would double check the equations and variables used to make sure they are applicable to the situation, and then use the appropriate formula to solve for the frequency heard by the motorcyclist.