Calculating Sound Intensity & Energy from Loudspeaker

[curiousM]

Homework Statement

A concert loudspeaker suspended high off the ground emits 27.0 W of sound power. A small microphone with a 0.700cm^2 area is 55.0 m from the speaker.


What is the sound intensity at the position of the microphone?



How much sound energy impinges on the microphone each second?

Homework Equations

I = P/a

I1 /I2 =R2^2 / R1^2

The Attempt at a Solution

I tried this as the solution

27W / (pi * (55m^2)) = .00284W/m^2. The answer is incorrect.

I could not answer question 2 since it is realted to question 1. PLEASE HELP

 

[Jhero]

Hello, thank you for your post. I can assist you with finding the correct solution to this problem.

First, let's review the equations that you listed. The equation I = P/a is the correct equation to use for finding the sound intensity at the position of the microphone. However, the equation I1 /I2 =R2^2 / R1^2 is not necessary for this problem.

To find the sound intensity, we need to divide the sound power (P) by the area (a) of the microphone. The area of the microphone is given as 0.700 cm^2, which we need to convert to m^2. This can be done by dividing by 10000, since 1 cm^2 = 0.0001 m^2. So, the area of the microphone in m^2 is 0.000007 m^2.

Now, we can plug in the values into the equation I = P/a:

I = 27 W / 0.000007 m^2 = 3.86 x 10^6 W/m^2

Therefore, the sound intensity at the position of the microphone is 3.86 x 10^6 W/m^2.

To find the amount of sound energy impinging on the microphone each second, we can use the formula:

Energy = Power x Time

We already know the power (27 W), but we need to find the time. The time can be found by dividing the distance (55 m) by the speed of sound in air, which is approximately 343 m/s.

Time = 55 m / 343 m/s = 0.16 seconds

Now, we can plug in the values into the formula:

Energy = 27 W x 0.16 s = 4.32 Joules

Therefore, the amount of sound energy impinging on the microphone each second is 4.32 Joules.

I hope this helps you understand the correct solution to this problem. Let me know if you have any further questions.