Question

A 0.71 W point source emits sound waves isotropically. Assuming that the energy of the waves is conserved, find the intensity (a)1.4 m from the source and (b)2.6 m from the source.

Answer 1

(a) 2.88×10⁻² W/m²

(b) 8.36×10⁻³ W/m²

Step-by-step explanation:

The intensity of sound from an isotropic point source, with distance L is given as

I = P/(4πL²) .................................... Equation 1

Where I = intensity of sound, P = Power from the source, L = length, π = pie.

(a)

1.4 m from the source.

I = P/(4πL²)

Given: P = 0.71 W, L = 1.4 m, π = 3.14.

Substitute into equation 1

I = 0.71/(4×3.14×1.4²)

I = 0.71/24.6176

I = 0.0288 W/m².

I = 2.88×10⁻² W/m²

(b) 2.6 m from the source.

Given: P = 0.71 W, L = 2.6 m, π = 3.14

Substitute into equation 1

I = 0.71/(4×3.14×2.6²)

I = 0.71/84.9056

I = 0.00836 W/m²

I = 8.36×10⁻³ W/m²