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  • A uniform rope of length  and mass <img alt="6 \mathrm{~kg}" src="https://entrancecor

A uniform rope of length 12 \mathrm{~m} and mass 6 \mathrm{~kg} hangs vertically from a rigid support. A block of mass 2 \mathrm{~kg} is attached to the free end. A transverse pulse of wavelength 0.06 \mathrm{~m} is produced at the lowers and of the rope. What is the wavelength of the pulse when it reaches the top of the rope-

Option: 1

0.06 \mathrm{~m}


Option: 2

0.12 \mathrm{~m}


Option: 3

0.09 \mathrm{~m}


Option: 4

None of these


Answers (1)

best_answer

$$ \begin{aligned} v=\frac{T}{\mu} \Rightarrow \frac{V_{\text {top }}}{V_{\text {bottom }}} & =\sqrt{\frac{V_{T}}{V_{B}}}=\sqrt{\frac{6+2}{2}}=2 \\ \lambda_{\text {top }}=\lambda_{\text {bottom }} \times 2 & =0.06 \times 2 \\ & =0.12 \mathrm{~m} \end{aligned}

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