Question

The sound level a distance of 37m

from an isotropic point source is 66dB.
What are (a) the intensity and (b) the total power radiated by the source?
(a) I = W/m^2
(b) p = W

Answer 1

To find the intensity and total power radiated by an isotropic point sound source, we use the formulas relating to decibels for intensity, and the formula for total power incorporating intensity and distance. Apply these to the given sound level of 66dB at 37m to find the requested values.

Step-by-step explanation:

The question is asking to determine the intensity and the total power radiated by the source of an isotropic point source, given the sound level at a specific distance. We can use the following formulas to solve the problem:

• The intensity (I) can be calculated using the formula for decibels (dB): I = (10^(L/10))×I0 where L is the sound level in dB and I0 is the reference intensity, typically 1×10-12 W/m2.
• To determine the total power (P) radiated by the source, we use the formula P = 4πr2I where r is the distance from the source and I is the intensity.

By applying these formulas for the sound level of 66dB at a distance of 37m:

1. Calculate the intensity:

I = (10^(66/10))×1×10-12 W/m2

1. Calculate the total power:
   P = 4π(37 m)2I

This will provide the answers for both (a) the intensity and (b) the total power radiated by the source.