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Multiple Choice
A sound source radiates sound waves in all directions. At a distance of 4 m from the source, you measure the wave intensity to be 0.06 W/m2. How much sound energy does the source emit in 1 hour if the power output is constant?
A
724 J
B
10,860 J
C
1.07 J
D
43,400 J
Verified step by step guidance
1
First, understand that the intensity (I) of a sound wave is defined as the power (P) per unit area (A). The formula is I = P/A.
Since the sound radiates in all directions, it forms a sphere around the source. The area (A) of a sphere is given by the formula A = 4πr², where r is the radius (distance from the source).
Substitute the given values into the intensity formula: I = P/(4πr²). Here, I = 0.06 W/m² and r = 4 m.
Rearrange the formula to solve for power (P): P = I × 4πr². Substitute the known values to find the power output of the source.
To find the total energy emitted in 1 hour, use the formula Energy = Power × Time. Convert 1 hour into seconds (1 hour = 3600 seconds) and multiply by the power calculated in the previous step.