A source of sound of frequency 50HZ is producing longitudinal waves in air. The amplitude of vibrations of air particles is 5mm and the speed of the wave is 330ms−1. Write the equation of the wave.
A
y=5×10−3sin[100πt−100πx33]
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B
y=0.05sin[220πt−πx3]
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C
y=0.05sin[110πt−2πx3]
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D
y=0.05sin[110πt−πx3]
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Solution
The correct option is Ay=5×10−3sin[100πt−100πx33] f=50HZ a=5mm=5×10−3m v=330ms−1
Now ω=2πf=2π×50=100πrads−1
Wavelength =λ=vf=33050=6.6m
Angular wavenumber =k=2πλ=2π6.6=10π33radm−1
The equation of the wave can be written as y=5×10−3sin[100πt−100πx33]
X and y are in metre t in seconds
Ans: y=5×10−3sin[100πt−100πx33]