Question

What is the intensity of a sound that has a level 7.00 dB lower than a (4.00 X 10⁻9 W/m²) sound?

a) (2.51 X 10⁻9 W/m²)
b) (2.60 X 10⁻9 W/m²)
c) (2.70 X 10⁻9 W/m²)
d) (2.80 X 10⁻9 W/m²)

Answer 1

To calculate the intensity of a sound that is 7 dB lower than a 4.00 × 10⁻⁹ W/m² sound, use the decibel formula to find the ratio and multiply it by the original intensity. The new intensity is a) 2.51 × 10⁻⁹ W/m².

Step-by-step explanation:

The question relates to the concept of sound intensity and its measurement in decibels (dB). Sound intensity level can be calculated using the following formula: ß(dB) = 10 log10 (I / I0), where I represents the intensity of the sound wave and I0 is the reference intensity, typically taken as 10⁻¹² W/m².

When the sound level decreases by 7 dB, we can calculate the new intensity using the inverse of this formula, taking into account that a decrease of 10 dB corresponds to a tenfold decrease in intensity.

To find the new intensity of a sound that is 7.00 dB lower than the original 4.00 × 10⁻⁹ W/m² sound, we apply the following steps:

1. Calculate the ratio of intensities corresponding to a 7 dB decrease: 10⁻⁰⁷/10 = 10⁻⁰⁷⁰.
2. Multiply the original intensity by this ratio: 4.00 × 10⁻⁹ W/m² × 10⁻⁰⁷⁰ = 2.51 × 10⁻⁹ W/m².

Therefore, the intensity of the sound is 2.51 × 10⁻⁹ W/m². The correct option is (a) 2.51 × 10⁻⁹ W/m².