Question

To practice Problem-Solving Strategy 16.1 Sound Intensity. A rescue team is searching for Andrew, a geologist who was stranded while conducting research in the mountains of Colorado. The team uses electronic listening devices in order to detect any shouts for help. The sound waves from his shouts reaching the base camp can be approximated by a sinusoidal wave with a frequency f = 540 Hz and displacement amplitude A = 4.00×10−8 m , where the sound wave properties are valid at the base camp where the measurements are being made. What sound intensity level will the rescue team measure from the frightened researcher? Assume the speed of sound is v=329m/s and the density of air rho = 1.24 kg/m3 . Calculate the bulk modulus B of air using the given values of the sound speed and air density. Express your answer numerically in Pascals.

Answer 1

A) I = 1.29 10⁻¹¹ W / m² , B) B = 1.34 10⁵ Pa

Step-by-step explanation:

The intensity of a wave is given by

I = P / A

Where the power of sound is

P = ½ ρ A v w² s₀²

Angular velocity and frequency are related.

w = 2π f

We replace

I = ½ ρ v 4π² f² s₀²

I = 2 π² ρ f² s₀²

Let's calculate

I = 2π² 1.24 329 (4.00 10⁻⁸)²

I = 1.29 10⁻¹¹ W / m²

Part B

The speed of sound is related to the properties of the medium where it propagates

v = √ B / ρ

B = ρ v²

Let's calculate

B = 1.24 329²

B = 1.34 10⁵ Pa