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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