Final answer:
The intensity at the speaker with a surface area of 0.05 m² producing 1W of power is 20 W/m². The distance at which the intensity becomes 0.1 W/m² can be found using the inverse square law for sound intensity.
Step-by-step explanation:
Understanding Sound Intensity and Distance ;The intensity of a sound is a measure of the power per unit area and is measured in watts per square meter (W/m²). When discussing a low-frequency speaker emitting 1 watt (W) of acoustical power iso tropically, the intensity at the surface of the speaker can be calculated using the formula I = P/A, where I is the intensity, P is the power, and A is the area.
For the given speaker with a surface area of 0.05 m², the intensity at the speaker is 1 W / 0.05 m² = 20 W/m². To find at what distance the intensity drops to 0.1 W/m², we use the inverse square law for sound intensity, I = P/(4πr²), where r is the radius or distance from the point source. Solving for r gives us the distance at which the intensity would be 0.1 W/m².