A uniform rope of mass $6\,kg$ hangs vertically from a rigid support. A block of mass $2\,kg$ is attached to the free end of the rope. A transverse pulse of wavelength $0.06\,m$ is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top is (in $m$ )
Diffcult
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The speed of transverse waves through a string of linear density $\mathrm{m}$ and tension $\mathrm{T}$ is given by
$\mathrm{v}=\sqrt{\mathrm{T} / \mathrm{m}}=\mathrm{f} \lambda$
Since, $f$ and $m$ are constants, $v$ and hence $\lambda$ is proportional to $\sqrt{\mathrm{T}}$. The tension at the bottom is 2 kg-wt, while at the top is $2+6$ $=8 \mathrm{\,kg}-\mathrm{wt} .$ If $\lambda_{1}$ and $\lambda_{2}$ are the wavelength at the bottom and the top respectively, we have:
$\left(\lambda_{2} / \lambda_{1}\right)=\sqrt{8 / 2}=2$
The wavelength at the top will be $=0.12 \mathrm{\,m}$
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