The equation of simple harmonic wave produced in the string under tension $0.4 \mathrm{~N}$ is given by…
The equation of simple harmonic wave produced in the string under tension $0.4 \mathrm{~N}$ is given by $\mathrm{y}=4 \sin (3 \mathrm{x}+60 \mathrm{t}) \mathrm{m}$. The mass per unit length of the string is
$10^{-3} \mathrm{~kg} \mathrm{~m}^{-1}$
$10^{-5} \mathrm{~kg} \mathrm{~m}^{-1}$
$10^{-3} \mathrm{~g} \mathrm{~cm}^{-1}$
$10^{-5} \mathrm{~g} \mathrm{~cm}^{-1}$
Solution
The standard equation of a wave can be written as
$\mathrm{y}=\mathrm{A} \sin (\mathrm{kx}+\omega \mathrm{t})$
Speed of wave $\mathrm{V}=\frac{\omega}{\mathrm{k}}=\frac{60}{3}=20 \mathrm{~m} / \mathrm{s}$
Also, $V=\sqrt{\frac{T}{m}}$
$\therefore \mathrm{m}=\frac{\mathrm{T}}{\mathrm{V}^2}=\frac{0.4}{400}=10^{-3} \mathrm{~kg} \mathrm{~m}^{-1}$