Question

A microphone receiving a pure sound tone feeds an oscilloscope, producing a wave on its screen. If the sound intensity is originally (2.00 X 10⁻5 W/m²), but is turned up until the amplitude increases by 30.0%, what is the new intensity?

a) (2.60 X 10⁻5 W/m²)
b) (2.60 X 10⁻4 W/m²)
c) (2.20 X 10⁻5 W/m²)
d) (2.20 X 10⁻4 W/m²)

Answer 1

The new sound intensity, after increasing the amplitude by 30.0%, is 3.38 × 10-5 W/m², which does not match the given options. The intensity of a sound wave is proportional to the square of the amplitude, hence the increase by a factor of 1.30 squared.

Step-by-step explanation:

If the original sound intensity is 2.00 × 10-5 W/m² and the amplitude of the wave increases by 30.0%, we need to determine the new intensity. The intensity of a sound wave is proportional to the square of its amplitude. Therefore, if the amplitude increases by 30.0%, it becomes 1.30 times its original value.

Since the new amplitude is squared to get the new intensity, the calculation is as follows: New Intensity = Original Intensity × (1.30)2 = 2.00 × 10-5 W/m² × (1.69).

The new intensity is thus 2.00 × 10-5 W/m² × 1.69 = 3.38 × 10-5 W/m². However, this result does not match any of the options provided. It seems there is an error in the available options or in the question as presented.

New Intensity = Original Intensity x (1 + 0.30)^2

Plugging in the values, we get:

New Intensity = (2.00 x 10^-5) x (1 + 0.30)^2

Solving this equation gives us the answer.