Question

A very noisy chain saw operated by a tree surgeon emits a total acoustic power of 30.0 W uniformly in all directions Part A At what distance from the source is the sound level equal to 100 dB?art B At what distance from the source is the sound level equal to 55 dB?

Answer 1

To find the distance from the source where the sound level is equal to 100 dB, calculate the sound intensity and use the formula for sound level. Similarly, for the sound level of 55 dB, calculate the sound intensity.

Step-by-step explanation:

To find the distance from the source where the sound level is equal to 100 dB, we can use the formula:

Sound level = 10 * log10(I/I0)

where I is the sound intensity and I0 is the reference intensity.

For Part A, we want to find the distance where the sound level is 100 dB.

Since the emitted power is 30.0 W uniformly in all directions, we can calculate the sound intensity using the formula:

I = P / (4πr2)

where P is the power and r is the distance from the source.

By substituting the given values, we get:

I = 30.0 W / (4πr2)

Rearranging the formula to solve for r, we get:

r = sqrt(30.0 W / (4π*I))

Substituting I = I0 * 10(100/10), we can calculate the distance.

For Part B, we follow the same steps as Part A, but substitute I = I0 * 10(55/10) to calculate the distance when the sound level is 55 dB.