A sound wave in air has a frequency of 30 Hz and a displacement amplitude of 6-0 - 10-3 mm- For this sound wave the intensity is 2-64 - 10-x Wm-2- Find the value of x-

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Standard XII

Physics

Amplitude Variation

A sound wave ...

Question

A sound wave in air has a frequency of 30 Hz and a displacement amplitude of $6.0 \times 10^{- 3} m m$ . For this sound wave the intensity is $2.64 \times 10^{- x} W m^{- 2}$ . Find the value of x.

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Solution

Intensity $I$ of a plane wave of amplitude $A$ , frequency $f$ , travelling with a velocity of $v$ in a medium of density $ρ$ is given by ,
$I = 2 π^{2} f^{2} A^{2} ρ v$ ,
we have , $v = 335 m / s, ρ = 1.225 k g / m^{3}, f = 30 H z, A = 6.0 \times 10^{- 3} m m = 6.0 \times 10^{- 6} m$ ,
therefore , $I = 2 \times {3.14}^{2} \times 30^{2} \times (6.0 \times 10^{- 6})^{2} \times 1.225 \times 335 = 2.62 \times 10^{- 4} W / m^{2}$

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A sound wave in air has a frequency of 30 Hz and a displacement amplitude of 6.0×10−3mm. For this sound wave the intensity is 2.64×10−xWm−2. Find the value of x.

Intensity I of a plane wave of amplitude A , frequency f , travelling with a velocity of v in a medium of density ρ is given by , I=2π2f2A2ρv ,we have , v=335m/s,ρ=1.225kg/m3,f=30Hz,A=6.0×10−3mm=6.0×10−6m , therefore , I=2×3.142×302×(6.0×10−6)2×1.225×335=2.62×10−4W/m2

A sound wave in air has a frequency of 30 Hz and a displacement amplitude of $6.0 \times 10^{- 3} m m$ . For this sound wave the intensity is $2.64 \times 10^{- x} W m^{- 2}$ . Find the value of x.