Question

A point source at the origin emits sound of frequency 175 Hz uniformly in all directions. On the x-axis at x=100 m, the sound intensity is 1.40 * 10^-4 W/m^2 . 1. What is the power output of the source?
2. What is the intensity ( in SI units ) on the x-axis at x=160m?
3. What is the intensity in decibels on the x-axis at x=160m? 4. A steady wind is blowing at 5.00 m/s in the positive x-direction. An observe on a bicycle at x=200 m is moving along the x-axis in the negative direction ( i.e., towards the source of sound ) at a speed of 12.0 m/s. What frequency of sound does the cyclist hear?

Answer 1

Answer:

Multiple answers:

1. Power output P=17.59W

2.Intensity 160m I=17.6W/$m^{2}$

3. dB = 77.3

4. f=178.5 Hz

Explanation:

First one comes from the expression

$I=\frac{P}{4\pi r^{2} }$

where I is the intensity, P is the power and r is the radio of the spherical wave, or in this case, the distance x. I solved for the Power by multiplying Intensity with the area (4$\pi x^{2}$

Second one is done with:

$\frac{I_{2} }{I_{1} } =\frac{x^{2}_{1} }{x^{2} _{2}}$

Solving for Intensity 2, the result mentioned.

The third is simply computed with

$dB=10*log\frac{I}{10^{-12} }$

And finally the last one is done with doppler effect, taking into account the speed of the air as in 10ºC 337m/s.

$f=f_{initial} *(\frac{s+v_{receiver} }{s+v_{source} } )$

Where Finitial is the frequency emitted and s is the speed of the sound. The wind blowing in positive is, in principle, going away of the observer.