Question

A concert loudspeaker suspended high off the ground emits 34 W of sound power. A small microphone with a 1.0 cm2 area is 44 m from the speaker.Part A -What is the sound intensity at the position of the microphone?Express your answer in mW/m2and using two significant figures.I = _________mW/m2Part B -What is the sound intensity level at the position of the microphone?Express your answer in dB using two significant figures.β= _________dB

Answer 1

Answer:

Part A

I = 1.4 mW/m²  

Part B

β = 91.46 dB

Explanation:

Part A

Sound intensity is the power per unit area of sound waves in a direction perpendicular to that area. Sound intensity is also called acoustic intensity.

For a spherical sound wave, the sound intensity is given by;

                                            $I = \frac{P}{A}$

                                            $I = \frac{P}{4\pi r^{2}}$

Where;

P is the source of power in watts (W)

I is the intensity of the sound in watt per square meter (W/m2)

r is the distance r away

Given:

P = 34 W,

A = 1.0 cm²

r = 44 m

The sound intensity at the position of the microphone is calculated to be;

                                     $I = \frac{34}{4\pi (44)^{2}}$

                                     $I = \frac{34}{4\pi (44)^{2}}$

                                     I = 0.0013975 W/m²

                                 ≈  I = 0.0014 W/m² = 1.4 × 10⁻³ W/m²

                                     I = 1.4 mW/m²

The sound intensity at the position of the microphone is 1.4 mW/m².

Part B

Sound intensity level or acoustic intensity level is the level of the intensity of a sound relative to a reference value.  It is a a logarithmic quantity. It is denoted by β and expressed in nepers, bels, or decibels.

Sound intensity level is calculated as;  

                                    β $= 10log_{10}\frac{I}{I_{0}}$  dB

Where,

β is the Sound intensity level in decibels (dB)

I is the sound intensity;

I₀ is the reference sound intensity;

By pluging-in, I₀ is 1.0 × 10⁻¹² W/m²

           ∴        β $= 10log_{10}\frac{1.4 * 10^{-3} W/m^{2}}{1.0 * 10^{-12} W/m^{2}}$

                      β $= 10log_{10} (1.4 * 10^{9})$

                      β = 91.46 dB

The sound intensity level at the position of the microphone is 91.46 dB.