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

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

Step-by-step explanation:

First one comes from the expression

`I=(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:

`(I_(2) )/(I_(1) ) =(x^(2)_(1) )/(x^(2) _(2))`

Solving for Intensity 2, the result mentioned.

The third is simply computed with

`dB=10*log(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) *((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.