Question

A concert loudspeaker suspended high off the ground emits 29.0 W of sound power. A small microphone with a 0.900 cm² area is 51.0 m from the speaker.

Part A
What is the sound intensity at the position of the microphone? Express your answer with the appropriate units.

Answer 1

The sound intensity at the position of the microphone, 51.0 meters from a loudspeaker emitting 29.0 W of sound power, is calculated to be 8.89x10^-4 W/m² using the formula for the intensity of a spherical wave.

Step-by-step explanation:

Calculating Sound Intensity

To find the sound intensity at the microphone, we need to use the formula for the intensity of a spherical wave, which is:

I = P / (4πr^2)

Where:

• I is the sound intensity (W/m²)
• P is the sound power (W)
• r is the distance from the sound source (m)

In this case:

• P = 29.0 W
• r = 51.0 m

Plugging the values into the equation yields:

I = 29.0 W / (4π(51.0 m)^2)

I = 29.0 W / (4π*2601 m²)

I = 29.0 W / 32602.4 m²

I = 8.89×10⁻´ W/m²

Therefore, the sound intensity at the position of the microphone is 8.89×10⁻´ W/m².