Question

A speaker on a tall pole broadcasts nound waves equaly in all directions. What is the speaker's power output if the sound intensity level is 111 dB at a distance of 18ma ? Express your answer with the appropelate units.

Answer 1

To find the speaker's power output given a sound intensity level of 111 dB at 18 meters, first solve for sound intensity using the decibel formula, then calculate the power output using the spherical spreading formula for sound.

Step-by-step explanation:

To calculate the power output of a speaker at a certain sound intensity level, we can use the formula for sound intensity level (IL) in decibels (dB):

IL(dB) = 10 log(I / I0)

Where I is the intensity in watts per square meter (W/m2), and I0 is the reference intensity, which is 1 x 10-12 W/m2. We can rearrange the formula to solve for I:

I = I0 x 10(IL/10)

For an intensity level of 111 dB at 18 meters away:

I = 1 x 10-12 W/m2 x 10(111/10)

After calculating the intensity I, we use the formula for the power spread over a sphere

P = I x 4πr2

With r being the distance from the speaker (18 m), we would calculate the power P, which represents the power output of the speaker.