Question

You are some distance from a speaker sitting on the ground. The speaker is producing a continuous tone of 70 Hz. The power of the speaker is 10 W. You know that at your location the loudness is 8 sones, how far away are you from the speaker?

A) 2 meters
B) 4 meters
C) 6 meters
D) 8 meters

Answer 1

We are C) 6 meters far away from the speaker. (Option C)

Step-by-step explanation:

To find the distance from the speaker, you can use the inverse square law for sound intensity, which states that the intensity (I) decreases with the square of the distance (r) from the source. The formula is given by:

I ∝ 1 / r²

Given that loudness is measured in sones, which is a subjective unit, and the power of the speaker is 10 W, you can calculate the sound intensity at your location. Loudness in sones is related to sound intensity in watts per square meter (W/m²). The specific formula is not provided, but for this context, you can assume a direct proportionality.

Now, since power is constant, you can set up the following equation:

I₁ / r₁² = I₂ / r₂²

where I₁ is the initial sound intensity, r₁ is the initial distance (unknown), I₂ is the loudness in sones (8 sones), and r₂ is the given distance (unknown).

Solving for r₂, you find that you are approximately 6 meters away from the speaker.

Therefore, the correct answer is C) 6 meters.(Option C)