A string wave equation is given y=0.002 sin (300 t-15 x) and mass density is μ=frac{0.1, kg }{m} .

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14.Waves and Sound

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A string wave equation is given $y=0.002 \sin (300 t-15 x)$ and mass density is $\mu=\frac{0.1\, kg }{m}$. Then find the tension in the string, (in $N$)

A

$30$

B

$20$

C

$40$

D

$45$

(AIIMS-2019)

Solution

The given string wave equation is,

$y=0.002 \sin (300 t-15 x)$

From the above equation,

$\omega=300$

$k=15$

The wave speed is calculated as,

$v=\frac{\omega}{k}$

$=\frac{300}{15}$

$=20 m / s$

Also, the expression for the wave speed in the string is,

$v=\sqrt{\frac{T}{\mu}}$

$20=\sqrt{\frac{T}{0.1}}$

$T=0.1 \times 20^{2}$

$=40 N$

Standard 11

Physics

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