A uniform thin rope of length 12 , m and mass | vedclass

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(B) The speed of a transverse wave on a string is given by $v = \sqrt{\frac{T}{\mu}}$,where $T$ is the tension and $\mu$ is the mass per unit length.S

Vedclass · Accepted Answer

$12$

Vedclass · Answer

(B) The speed of a transverse wave on a string is given by $v = \sqrt{\frac{T}{\mu}}$,where $T$ is the tension and $\mu$ is the mass per unit length.Since the frequency $f$ of the wavetrain remains constant,$v = f \lambda$,which implies $v \propto \lambda$.At the lower end (bottom),the tension $T_1$ is due to the block of mass $m = 2 \, kg$:$T_1 = mg = 2g$.At the top of the rope,the tension $T_2$ is due to the block and the entire mass of the rope $M = 6 \, kg$:$T_2 = (M + m)g = (6 + 2)g = 8g$.Using the relation $\frac{\lambda_2}{\lambda_1} = \frac{v_2}{v_1} = \sqrt{\frac{T_2}{T_1}}$:$\lambda_2 = \lambda_1 \sqrt{\frac{8g}{2g}} = 6 	imes \sqrt{4} = 6 	imes 2 = 12 \, cm$.

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