A siren emits sound of intensity 1.6 W/m2 and frequency 1000 Hz. Speed of sound in air is330 m/s and density of air is 1.3 kg/m3. Amplitude of sound emitted by the siren is nearly:
Question
A siren emits sound of intensity 1.6 W/m2 and frequency 1000 Hz. Speed of sound in air is330 m/s and density of air is 1.3 kg/m3. Amplitude of sound emitted by the siren is nearly:
Solution
To find the amplitude of the sound emitted by the siren, we first need to find the intensity of the sound wave. The formula for intensity is:
I = (1/2) * ρ * v * ω^2 * A^2
where: I is the intensity, ρ is the density of the medium the sound is traveling through, v is the speed of sound in the medium, ω is the angular frequency, and A is the amplitude of the sound wave.
We can rearrange this formula to solve for A:
A = sqrt(I / ((1/2) * ρ * v * ω^2))
We know that I = 1.6 W/m^2, ρ = 1.3 kg/m^3, v = 330 m/s, and the frequency f = 1000 Hz.
The angular frequency ω is related to the frequency by the formula ω = 2πf, so ω = 2π * 1000 = 2000π rad/s.
Substituting these values into the formula for A, we get:
A = sqrt(1.6 / ((1/2) * 1.3 * 330 * (2000π)^2)) A = sqrt(1.6 / (845000π^2)) A = sqrt(1.6 / 845000 * 9.87) A = sqrt(0.00000189) A = 0.00137 m
So, the amplitude of the sound emitted by the siren is approximately 0.00137 meters, or 1.37 millimeters.
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