The intensity of the sound wave

Thread starter hidemi
Start date Feb 8, 2021
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Intensity Sound Sound wave Wave

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The intensity of sound waves is calculated using the formula I = 1/2 ρvR²w², where ρ is the density of air, v is the speed of sound, R is the amplitude, and w is the angular frequency. The user calculated an intensity of 0.16 W/m², which is significantly lower than the 32 W/m² threshold for potential hearing damage. Concerns were raised about prolonged exposure to even 0.16 W/m², suggesting it could still be harmful over extended periods. A rough calculation by another participant supports the user's initial answer but highlights the discrepancy with the expected value. The discussion emphasizes the importance of understanding sound intensity and its implications for hearing safety.

Feb 8, 2021

hidemi

Homework Statement: The speed of sound in air in 340 m/s, and the density of air is 1.2 kg/m^3. if the displacement amplitude of a 440 Hz sound wave is 10μm. what is the intensity of the wave?

Ans: 32 W/m^2

Relevant Equations: I = 1/2 ρvR²w²

I = 1/2 ρvR²w²

I = 1/2 *1.2kg/m³*340m/s*(10 x 10^-6m)²*(2π*440/s)²

I = 0.16 W/m²

This is my answer which does not match the given answer. Am I doing wrong?

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Feb 8, 2021

haruspex

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32W/m² is hearing damage in a matter of seconds. Even 0.16 for 30 min is ill-advised.
From a rough calculation, I agree with your answer.

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