If the pressure amplitude of a sound wave is halved, by what factor does the intensity of the wave change?
1 Answer
The intensity (I) of a sound wave of pressure amplitude (ΔPm) is given by
\(I=\frac{\Delta P_m^2}{2\rho v}\)
Where ρ is the density of medium and v is the velocity of the wave. When (ΔPm) is halved, then,
\(I'=\frac{\left(\Delta P'_m\right)^2}{2\rho v}=\frac1{2^2}\left(\frac{\left(\Delta P_m\right)^2}{2\rho v}\right)=\frac14I\)
Thus, intensity is reduced by 4 times is the pressure amplitude is halved.
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