# Doppler Shift

confusedinphys

## Homework Statement

You are standing by the roadside as a truck approaches, and you measure the dominant frequency of the truck noise at 1100 Hz. As the truck passes, the frequency drops to 950 Hz. What is the truck's speed?

## Homework Equations

f'= f (vsound)
-------------------
(vsound-velocity of source)

1100 = 950(340)
------
(340-vs)

## The Attempt at a Solution

I rearrange for velocity of source and get 47 m/s, but my book says 25 m/s

## Answers and Replies

Staff Emeritus
Science Advisor
f'= f (vsound)
-------------------
(vsound-velocity of source)
Is one relationship - in this case for frequency change of a sound moving toward the listener/receiver for which there is an increase in frequency

So f' = f (vs/(vs-v)) = 1100 Hz,

for the case where the source passes and is traveling away from the listener/receiver

f' = f (vs/(vs+v)) = 950

Take on equation and rearrange for f

one should obtain

1100 = 950 $$\big(\frac{v_s\,+\,v}{v_s\,-\,v}\big)$$

Homework Helper
Gold Member
Here, you have two unknowns. 1100 Hz, and 950 Hz are both frequencies you observe, neither is the actual frequency of the source. That is, they are both values of f', one for when the truck is approaching you, the other for when the truck is moving away from you.

So, as I said, their are two variables you do not know, the source frequency, and the speed of the source.

HINT: Since you have two unknowns here, you are going to need two equations to solve this problem? Using the doppler shift formula you have above, can you set up two equations corresponding to this situation?

EDIT: (Astronuc you beat me to it!)

confusedinphys
I really have no idea what you mean by two eqautions here, can someone fill me in?

Science Advisor
Homework Helper
Gold Member
Look back at Astronuc's post.
Can you summarize his suggestion?