How Far Is the Sound Level from a Loudspeaker at Different Decibels?

[ultimateguy]

Homework Statement

A loudspeaker uses 65W of electrical power at 1kHz and converts this electrical power into acoustical power with an efficiency of 0.75%. Determine the distance at which the sound level is a) at the threshold of pain (120db) and b) 60db. Assume the loudspeaker emits sound waves uniformly in all directions.

Homework Equations

beta = 10log(I/Io)
I = P/4pir^2

The Attempt at a Solution

I know how to solve this usually, but what is throwing me off is the inclusion of the frequency of the electrical power.
In the second equation, I used a power of 0.0075(65)=0.4875W. And did the calculations. I obtained 0.197m for a) and 197m for b).

Is this right, or do I need to include the frequency somehow?

 

[Mindscrape]

Good question. I don't think that the frequency comes into it because I don't see any sort phase information, which I think you would need if there was some kind of frequency dependence. So yeah, I think you are right in just using the amplitude.

 

[m2003]

As a scientist, it is important to consider all relevant factors when solving a problem. In this case, the frequency of the electrical power is not directly relevant to the calculation of the distance at which the sound level is a) at the threshold of pain and b) 60db. The equations used are correct and the distances calculated seem reasonable. However, it is important to note that the efficiency of the loudspeaker may vary at different frequencies, which could potentially affect the accuracy of the calculated distances. Additionally, other factors such as environmental conditions and the directionality of the loudspeaker may also impact the sound level at a given distance. It may be worthwhile to conduct further experiments or research to validate the calculated distances and determine any potential sources of error.