Why Is Jim Hearing a Different Frequency from the Ambulance Siren?

[roam]

Homework Statement

An ambulance is traveling at 72.0 km/h towards an intersection. Jim stops his car to give way to the ambulance as shown in the diagram below. In the diagram, the angle θ = 41.0 °.
The ambulance has a siren which produces sound at a frequency of 2.1 kHz. Assume the speed of sound in air is 335.0 m/s.

[PLAIN]http://img693.imageshack.us/img693/7959/amburightjimrest.gif

What is the doppler shift (Δf = f ′ – f ) heard in the siren sound by Jim, when Jim and the ambulance are positioned as shown on the diagram above?

(correct answer: 0.0991 kHz)

Homework Equations

General Doppler-shift expression: $$f'=\left( \frac{v+v_o}{v-v_s} \right)f$$

The Attempt at a Solution

$$f'=\left( \frac{v+v_o}{v-v_s} \right)f= \left( \frac{335}{335-72} \right)2.1=2.62$$

f'-f=2.62-2.1= 0.52

Why am I not getting the right answer? Does this have something to do with the angle? All the examples in my textbook deal with situations where the observer or the source are moving directly toward one another, there are no examples with angles. Any help is appreciated.

 

[Dweirdo]

First, you have to convert km/h to m/s.
Next, does the source advance in the y direction?? does it advance in the X direction?
what is the source's velocity in y direction(if it has any..)?? what is the source's velocity in the X direction?
what should you plug in the equation?

 

[roam]

First, you have to convert km/h to m/s.
Next, does the source advance in the y direction?? does it advance in the X direction?
what is the source's velocity in y direction(if it has any..)?? what is the source's velocity in the X direction?
what should you plug in the equation?

The source is moving in the x direction but the sound that reaches the driver has both x and y component.

v_x=335cos41=252.8
v_y=335sin41=219.7

The resultant is:

$$\sqrt{252.8^2+219.7^2}=334.9$$

$$\frac{334.9}{334.9-20}2.1=1.27$$

then why do I still get the wrong answer?

 

[Dweirdo]

Your mixing some stuff,
the velocity of the source is 20 m/s to the left, no doubt about that.
the velocity of sound in air is 335 m/s still no doubt about that.
You need to take the component of the velocity in the direction connecting the ambulance with the car.
to get that component it's 20*cos41 and you'll get the right answer..

 

[roam]

Thank you! I get it now!