Question 431: Waves

Question

The equation of simple harmonic wave produced in the string under tension $$0.4 \mathrm{~N}$$ is given by $$\mathrm{y=4 \sin (3 x+60 t) ~m}$$. The mass per unit length of the string is

Accepted Answer

The standard equation of a wave can be written as
$$\mathrm{y}=\mathrm{A} \sin (\mathrm{kx}+\omega \mathrm{t})$$
Speed of wave $$V=\frac{\omega}{k}=\frac{60}{3}=20 \mathrm{~m} / \mathrm{s}$$
$$\begin{aligned}
& 	ext { Also, } \mathrm{V}=\sqrt{\frac{\mathrm{T}}{\mathrm{m}}} \
& 	herefore \quad \mathrm{m}=\frac{\mathrm{T}}{\mathrm{V}^2}=\frac{0.4}{400}=10^{-3} \mathrm{~kg} \mathrm{~m}^{-1}
\end{aligned}$$

Answer

$$10^{-3} \mathrm{~kg} \mathrm{~m}^{-1}$$

Answer

$$10^{-5} \mathrm{~kg} \mathrm{~m}^{-1}$$

Answer

$$10^{-3} \mathrm{~g} \mathrm{~cm}^{-1}$$

Answer

$$10^{-5} \mathrm{~g} \mathrm{~cm}^{-1}$$

Waves

The equation of simple harmonic wave produced in the string under tension $0.4 \mathrm{~N} is given by \mathrm{y=4 \sin (3 x+60 t) ~m}$. The mass per unit length of the string is

Choose the correct answer: