Apoint 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?

Multiple answers:

1. Power output P=17.59W

2.Intensity 160m I=17.6W/

3. dB = 77.3

4. f=178.5 Hz

Explanation:

First one comes from the expression

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

Second one is done with:

Solving for Intensity 2, the result mentioned.

The third is simply computed with

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

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.

see the picture for the vector

the magnitude of the vector by pythagorean theorem

r = √( (-10)^2 + (3)^2 ) = √109

magnitude = √109 units

the direction angle between vector and x-axis is

tan^(-1)(3/10) = 16.699

so the direction is approximately 16.7 degrees north of west