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Answer :
The loudness of the sound from the speaker will be 97.5 dB at a distance of 2.9 mm from the speaker.
The loudness of a sound wave can be measured in decibels (dB) and is related to the power of the wave. The formula to calculate the sound intensity level (SIL) in decibels is SIL = 10 log(I/I₀), where I is the sound intensity and I₀ is the reference intensity, which is usually taken to be the threshold of human hearing, 1 × 10⁻¹² W/m².
To calculate the distance at which the loudness of the sound from the speaker will be 97.5 dB, we can use the formula for sound intensity, which is given by I = P/4πr², where P is the power of the wave and r is the distance from the source.
Since the speaker produces 1 W of power, we can substitute P = 1 W into the formula to get I = 1/4πr². Setting SIL = 97.5 dB, we have:
97.5 = 10 log(I/I₀)
9.75 = log(I/I₀)
I/I₀ = 10^9.75 = 7.94 × 10⁹
Substituting this value for I/I₀ into the formula for sound intensity and solving for r, we get: 7.94 × 10⁹ = 1/4πr²
r = sqrt(1/(4π × 7.94 × 10⁹)) = 0.0029 m or 2.9 mm.
To know more about sound wave, refer here:
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