Final answer:
The intensity of a sound at 63 dB can be calculated using the formula I = I0 × 10^(dB/10), with I0 being the reference intensity. The total power radiated by the source is found by multiplying the intensity by the surface area over which the power is spread. To find the distance where intensity is 0.1 W/m^2, one would solve for r in the formula I = P / (4πr^2).
Step-by-step explanation:
The sound level at a distance of 20 m from an isotropic point source is 63 dB. To find the intensity (I) and the total power (P) radiated by the source, we need to use the formula for sound intensity levels:
I = I0 × 10(dB/10)
where I0 is the reference intensity, typically set at 1 x 10-12 W/m2 for sound in air, and dB is the sound intensity level in decibels. For 63 dB, this would give us:
I = 1 x 10-12 × 10(63/10)
To find the total power emitted by the source, we can use the formula P = I × A, where A is the surface area over which the power is spread. Since the source is isotropic, the power spreads over the surface area of a sphere with radius r (20 m in this case). The surface area (A) = 4πr2.
Regarding the second part of the question, to find the distance at which the intensity is 0.1 W/m2 from the same isotropic source, we use:
I = P / (4πr2)
From the equation above, when I is 0.1 W/m2, we can solve for r to find the distance from the speaker where this intensity occurs.