Calculating Power at source from Intensity at distance R

• dmoney123
WIn summary, the intensity level of sound entering the window space from the loudspeaker, located 46 m away, is 42 dB. The acoustic power output of the loudspeaker is approximately 4.2*10^-4 W. The threshold of hearing is 1.0 × 10-12 W/m2.
dmoney123

Homework Statement

An enclosed chamber with sound absorbing walls has a 2.0 m × 1.0 m opening for an outside window. A loudspeaker is located outdoors, 46 m away and facing the window. The intensity level of the sound entering the window space from the loudspeaker is 42 dB. Assume the acoustic output of the loudspeaker is uniform in all directions and that acoustic energy incident upon the ground is completely absorbed and therefore is not reflected into the window. The threshold of hearing is 1.0 × 10-12 W/m2. The acoustic power output of the loudspeaker is closest to

Homework Equations

A=10log(I/I_0)

I_0=1*10^-12 W/m^2

The Attempt at a Solution

We know

42=10log(I/1*10^-12)
10^4.2 (1*10^-12)=I
I=1.5849*10^-8 W/m^2

we also know that it is received in an area of 2m^2

I don't know how to find the ratio for the source. ie distance=0

If you treat it like a point source then... i don't know.

Figured it out. (4 pi r^2)=P/I where r=46.

P=4.2*10^-4

berkeman

What is the equation for calculating power at source from intensity at distance R?

The equation is P = I * 4 * pi * R^2, where P is power at source, I is intensity at distance R, and pi is a mathematical constant.

How do I determine the intensity at a specific distance from the source?

To determine intensity at a specific distance, you can use the equation I = P / (4 * pi * R^2), where I is intensity, P is power at source, and R is the distance from the source.

Can I use this equation for any type of radiation or wave?

Yes, this equation can be used for any type of radiation or wave as long as the intensity and distance are measured in consistent units.

What are some factors that can affect the accuracy of calculating power at source from intensity at distance R?

Some factors that can affect the accuracy of this calculation include environmental factors such as absorption or scattering of the radiation, as well as measurement errors.

Can this equation be used for point sources as well as extended sources?

Yes, this equation can be used for both point sources and extended sources. However, for extended sources, the intensity should be averaged over the entire source area.

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