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Chapter 16: Q. 38 (page 452)

What are the sound intensity levels for sound waves of intensity (a) 3.0 * 10-6 W/m2 and (b) 3.0 * 10-2 W/m2 ?

Short Answer

Expert verified

Part a

The sound intensity level for a sound wave of intensity $3.0 \times 10^{- 6} W / m^{2}$ is $65 d B$ .

Part b

The sound intensity level for a sound wave of intensity $3.0 \times 10^{- 2} W / m^{2}$ is $105 d B$ .

Step by step solution

01

Given information

The intensity of the sound wave is $a) 3.0 \times 10^{- 6} W / m^{2}$ and $b) 3.0 \times 10^{- 2} W / m^{2}$ .

02

Part a

The sound intensity level is given by $β = (10 d B) \log_{10} (\frac{I}{I_{0}})$ .

Substitute the given values

$β = (10 d B) \log_{10} (\frac{3.0 \times 10^{- 6}}{1.0 \times 10^{- 12}}) β \approx 65 d B$

Therefore, the sound intensity level for a sound wave of intensity $3.0 \times 10^{- 6} W / m^{2}$ is $65 d B$ .

03

Part b

The sound intensity level is given by $β = (10 d B) \log_{10} (\frac{I}{I_{0}})$ .

Substitute the given values

$β = (10 d B) \log_{10} (\frac{3.0 \times 10^{- 2}}{1.0 \times 10^{- 12}}) β \approx 105 d B$

Therefore, the sound intensity level for a sound wave of intensity $3.0 \times 10^{- 2} W / m^{2}$ is $105 d B$ .

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