Question 1: Waves

Question

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

Accepted Answer

Given, wave equation, $y=0.002 \sin (300 t-15 x)$
Mass density, $\mu=0.1 \mathrm{~kg} / \mathrm{m}$
Comparing the given wave equation with
$y=a \sin (\omega t-k x)$, we have $\omega=300, k=15$
$	herefore$ Velocity of wave,
$v=\frac{\omega}{k}=\frac{300}{15}=20 \mathrm{~m} / \mathrm{s}$
Wave speed in string is also given by
$v=\sqrt{\frac{T}{\mu}}$
where, $T=$ tension in the string and $\mu=$ mass per unit length of string
$	herefore 20=\sqrt{\frac{T}{0.1}} \Rightarrow 400=\frac{T}{0.1} \Rightarrow T=40 \mathrm{~N}$

Answer

30 N

Answer

20 N

Answer

40 N

Answer

45 N

Waves

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

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