Sound Intensity Help: Calculate Intensity & Level at 48m Mic Position

[hellokitty]

Homework Statement

A concert loudspeaker suspended high off the ground emits 36 W of sound power. A small microphone with a 1.0 cm^2 area is 48m from the speaker.

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

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

Homework Equations

I don't know where to begin. Which formulas do I use?
* I=P/4(pie)r^2 ?
*B(beta)= 10log( I/ Io)?

But it says the microphone is 1.0cmsquared area is 48 m? What does the distance x=48m fall into any of the formulas?

The Attempt at a Solution

I Cannot solve this problem...help!

 

[tiny-tim]

A concert loudspeaker suspended high off the ground emits 36 W of sound power. A small microphone with a 1.0 cm^2 area is 48m from the speaker.

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

What is the sound intensity level at the position of the microphone?
…
I don't know where to begin. Which formulas do I use?
* I=P/4(pie)r^2 ?
*B(beta)= 10log( I/ Io)?
…
What does the distance x=48m fall into any of the formulas?

hello hello kitty kitty!

(have a π: and a beta: ß or a different beta: β )

I don't know what the definitions of sound intensity and sound intensity level are , but the 48m is obvously the r in 4πr².

The reason for the 4πr² in the formula is that it's the surface area of a sphere of radius r …

the power P is spread over the whole surface area, so the power per area is P/4πr².

 

[thomate1]

As a scientist, it is important to have a thorough understanding of the concepts and equations involved in a problem before attempting to solve it. In this case, we are dealing with sound intensity and sound intensity level. Sound intensity is defined as the power of sound per unit area and is measured in watts per square meter (W/m^2). The equation for sound intensity is I = P/A, where P is the sound power and A is the area.

In this problem, we are given the sound power (P = 36 W) and the area of the microphone (A = 1.0 cm^2 = 0.0001 m^2). However, we also need to take into account the distance between the speaker and the microphone, as sound intensity decreases with distance. The formula for this is I = P/(4πr^2), where r is the distance between the speaker and the microphone in meters.

Therefore, to calculate the sound intensity at the position of the microphone, we can plug in the given values into the equation:

I = 36 W / (4π * (48 m)^2) = 0.005 W/m^2

To calculate the sound intensity level, we can use the formula B = 10log(I/Io), where Io is the reference sound intensity of 10^-12 W/m^2. This will give us the sound intensity level in decibels (dB). Again, we can plug in the previously calculated value for sound intensity (I = 0.005 W/m^2) into the equation:

B = 10log(0.005/10^-12) = 84.77 dB

Therefore, the sound intensity at the position of the microphone is 0.005 W/m^2 and the sound intensity level is 84.77 dB. It is important to note that the microphone's small area does not affect the calculation of sound intensity or sound intensity level, as these values are independent of the size of the receiving surface.