Question

question (1 point) you double your distance from a sound source that is radiating equally in all directions. what happens to the intensity of the sound? a) it reduces to one - fourth its original value. b) it reduces to one - half its original value. c) it reduces to one - sixteenth its original value. d) none of the above.

Explanation:

Step1: Recall Intensity Formula

Sound intensity \( I \) from a point source (radiating equally in all directions) follows the inverse - square law: \( I=\frac{P}{4\pi r^{2}} \), where \( P \) is the power of the source and \( r \) is the distance from the source.

Step2: Analyze Initial and Final Intensity

Let the initial distance be \( r_1 = r \) and the initial intensity be \( I_1=\frac{P}{4\pi r^{2}} \). When the distance is doubled, \( r_2 = 2r \). The final intensity \( I_2=\frac{P}{4\pi(2r)^{2}}=\frac{P}{4\pi\times4r^{2}} \).

Step3: Find the Ratio of Intensities

Divide \( I_2 \) by \( I_1 \): \( \frac{I_2}{I_1}=\frac{\frac{P}{4\pi\times4r^{2}}}{\frac{P}{4\pi r^{2}}}=\frac{1}{4} \). So \( I_2=\frac{1}{4}I_1 \), meaning the intensity reduces to one - fourth its original value.

Answer:

a) It reduces to one - fourth its original value.