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
  1. $10^{-3} \mathrm{~kg} \mathrm{~m}^{-1}$
  2. $10^{-5} \mathrm{~kg} \mathrm{~m}^{-1}$
  3. $10^{-3} \mathrm{~g} \mathrm{~cm}^{-1}$
  4. $10^{-5} \mathrm{~g} \mathrm{~cm}^{-1}$

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, $V=\sqrt{\frac{T}{m}}$ $\therefore \mathrm{m}=\frac{\mathrm{T}}{\mathrm{V}^2}=\frac{0.4}{400}=10^{-3} \mathrm{~kg} \mathrm{~m}^{-1}$

Asked in: MHT CET 2021 (21 Sep Shift 2)

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