Question

A blast gives a sound of intensity 0.8W/m^2 and frequency 1kHz. If the density of air is 1.3kg/m^3 and speed of sound in air is 330m/s, the amplitude of the sound wave is approximately?
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Answer 1

The value of amplitude in given question is    Δs = 9.71 μm

Step by step explanation:

$\textbf{Equation of intensity with respect to displacement amplitude =}$

$\textbf{\large The intensity of Sound wave : I =}2\pi^2\rho f^2v\Delta s^2\\\\So, \Delta s = \sqrt \frac{I}{2\pi^2\rho f^2v}$       (equation 1)

Here

Intensity of wave I = 0.8 $Wm^-^2$

Frequency of wave f = 1 kHz

Density of air ρ = 1.3 $kgm^-^3$

Speed of sound in air v = 330 $ms^-^1$

Displacement amplitude Δs = (unknown)

Putting all the values of given quantities  in equation 1

$\Delta s = \sqrt \frac{0.8}{2\pi^2\times 1.3 \times (1000)^2\times 330}$             (Solving this calculation , we get)

$\Delta s = \sqrt (0.9447)\times 10^-^1^0 = 0.971 \times 10^-^5 m$

$\textbf{\Large So, The value of amplitude = 9.71 }\mu m$