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A Sound wave of frequency $845 \mathrm{~Hz}$ travels with the speed of $332 \mathrm{~m} / \mathrm{s}$ along the Positive x-axis, Each point of the wave moves to and fro through a total distance of $8 \mathrm{~cm}$ . What will be the mathematical expression of this travelling wave?
Option: 1
$160\mathrm{~m}^{-1}$

Option: 2
$160\mathrm{~m}^{-1}$

Option: 3
$170\mathrm{~m}^{-1}$

Option: 4
$180\mathrm{~m}^{-1}$

Answers (1)

best_answer

Given, frequency of sound wave $n=845 \mathrm{~Hz}$

Speed of sound wave $V=332 \mathrm{~m} / \mathrm{s}$

Total distance $=8 \mathrm{~cm}$

Amplitude $A=4 \mathrm{~cm}=4 \times 10^{-2}=0.04 \mathrm{~m}$

${\omega}=2\pi n= 2\times 3.14\times 845$

${\omega}=\frac{1690 \times 314}{100}=169 \times 314 \times 10^{-1} \\$

$\omega=53066 \times 10^{-1} \\$

$\omega=5.3 \times 10^3 \mathrm{rad} / \mathrm{s} \\$

$K=\frac{\omega}{v}=\frac{5.3 \times 10^3}{332} \\$

$K=0.159 \times 10^3 \\$

$K=159 \mathrm{~m}^{-1}$

mathematical expression of the given travelling wave

$=A \sin (k n-w t) \\$

$=0.04 \sin \left[159 x-\left(5.3 \times 10^3\right) t\right]$

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