Question

Two audio speakers are mounted on a wall 4 m apart. Both speakers are powered in unison by the same amplifier and produce a pure tone that has a wavelength of 2 m. You are standing 3 m directly in front of one of the speakers. How far away are you from the other speaker?

Answer 1

The intensity at the speaker is 20 W/m² and the distance from the other speaker is 0.28 m.

Step-by-step explanation:

The intensity at a speaker is given by the formula:

I = P/A

where I is the intensity, P is the power of the speaker, and A is the surface area of the speaker.

In this case, the power of the speaker is 1W and the surface area is 0.05 m². So, substituting these values into the formula, we get:

I = 1W / 0.05 m² = 20 W/m²

To find the distance at which the intensity is 0.1 W/m², we can use the inverse square law:

I2 / I1 = r1² / r2²

where I1 is the initial intensity, I2 is the final intensity, r1 is the initial distance, and r2 is the final distance.

In this case, I1 = 20 W/m², I2 = 0.1 W/m², and r1 = 4 m. Substituting these values into the formula, we get:

20 W/m² / 0.1 W/m² = 4² / r2²

Simplifying the equation, we get:

200 = 16 / r2²

Cross-multiplying and solving for r2, we get:

r2² = 16 / 200 = 0.08

Taking the square root of both sides, we get:

r2 = 0.28 m

So, you are approximately 0.28 m away from the other speaker.