First slide

Travelling wave

Question

A uniform thin rope of length 12 m and mass 6 kg hangs vertically from a rigid support and a block of mass 2 kg is attached to its free end. A transverse short wave-train of wavelength 6 cm is produced at the lower end of the rope. What is the wavelength of wavetrain (in cm) when it reaches the top of the rope?

Moderate

A

12
B

6
C

3
D

9

Solution

$\begin{array}{l} V = f λ \\ \Rightarrow V \propto λ \\ A l s o, V = \sqrt{\frac{T}{μ}} \\ ∴ \sqrt{T} \propto λ \\ \Rightarrow \frac{\sqrt{2}}{\sqrt{2 + 6}} = \frac{6}{λ} \\ \Rightarrow λ = 6 (2) = 12 cm \end{array}$

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