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A sound wave in air at 20°C has a frequency of 320 Hz and a displacement amplitude of 5.00×10-3mmFor this sound wave calculate the (a) pressure amplitude (in Pa); (b) intensity W/m2(c) sound intensity level (in decibels).

Short Answer

Expert verified

A) 4.15Pa b) 0.02086W/m2 c) 103.2dB

Step by step solution

01

STEP 1 Instantons pressure fluctuation for sinusoidal sound wave:

Formula isP(x,t)=BkAsin(kx-ϖt) where,P The pressure, B Bulk modulus of the medium, A Displacement amplitude, k the wave number, c The position at which we want the pressure, t time,ϖ=2πfangular frequency of the wave

P(x,t)=BkAsin(kx-ϖt)is maximum when sin has maximum value,

the maximum value for sin function =1Pmax=BKA

P is the maximum pressure, B is Bulk modulus of the medium, A is the displacement amplitude,k=2πλ the wave number

02

Calculate the pressure amplitude

Bair=1.42×105Pav=344m/sk=2πλv=λT=λfλ=vfk=2πλ=2πv=2πfv=2×3.14×320Hz344m/s=5.845rad/mPmax=BkA=B×2πfvA=1.42×1052×3.14×3203445×10-3×10-3=4.15Pa

Therefore, the pressure amplitude is 4.15 Pa

03

Calculate the Intensity of a sinusoidal sound wave in a fluid

I=12BϖkA2=12ρB×ϖ2A2

B is Bulk modulus of the medium, A is Displacement amplitude, k The wave number,The density of medium,ϖ=2πfangular frequency of the wave

I=12BϖkA2=12B×2πfkA2=121.42×1052×3.14×3205.8455×10-3×10-3=0.02026W/m2

Therefore, the intensity is0.02026W/m2

04

Calculate the sound intensity level in decibels

The decibel scaleβ=(10dB)logII0were,β sound intensity level, I intensity of sound wavel0=10-12 is the reference intensity.

Substitute the value in equationβ=10dBlogll0

10dBlog0.0208610-12=103.2dB

Therefore, the intensity in decibels is 103.2dB

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