- #1

Nishikino Maki

- 18

- 0

## Homework Statement

Here is the problem: http://faculty.kfupm.edu.sa/PHYS/kuhaili/doppler_problem.htm

{Mentor's edit: Here's the text copied from the url:

A fire engine moving to the right at 40 m/s sounds its horn ( frequency 500 Hz ) at the two vehicles shown in the figure. The car is moving to the right at 30 m/s, while the van is at rest.

(a) What frequency is heard by the passengers in the car?

(b) What is the frequency as heard by the passengers in the van?

(c) When the fire engine is 200 m away from the car and 250 m from the van, the passengers in the car hear a sound intensity of 90 dB. At that moment, what intensity level is heard by the passengers in the van?

}

## Homework Equations

Doppler Effect:

[itex]f' = f\frac{v±v_o}{v∓v_s}[/itex]

Intensity:

[itex]I = \frac{P}{4\pi r^2}[/itex]

Sound level:

[itex]\beta = 10 \log \frac{I}{10^{-12}} [/itex]

## The Attempt at a Solution

I actually got answers for the problem, however, this was an even problem and I could not check my answers anywhere.

Part a:

[itex]f'=500(\frac{343 - 30}{343 - 40})[/itex]

This turned out to be 516.5 Hz

Part b:

[itex]f'=500(\frac{1}{1 - \frac{40}{343}})[/itex]

This was 566 Hz

Part c:

For this part I assumed that everything was standing still, and just used intensity and decibel formulas.

[itex]90=10 \log \frac{I}{10^{-12}}[/itex]

[itex]I = 10^{-3}[/itex]

[itex]P = I*4\pi 200^2[/itex]

[itex]I_2 = \frac{P}{4\pi 250^2}[/itex]

[itex]\beta = 10\log \frac{I_2}{10^{-12}}[/itex]

[itex]\beta = 88 dB[/itex]

Last edited by a moderator: