JEE Main · 2020 · 03 Sep 2020 · Shift 1 · Waves & Sound

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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 and the rope. What is the wavelength of the wave train (in cm) when it reaches the top of the rope?

(A)6
(B)12✓ Correct
(C)3
(D)9

Answer: (B)

Solution

The wave speed on the rope is

v = T / μ

, and because the frequency set at the source is fixed, the wavelength scales with the speed. At the lower end the tension is just the block's weight,

T_{1} = 2 \times 10 = 20

N, while at the top it also carries the rope,

T_{2} = (2 + 6) \times 10 = 80

N. Thus

\frac{v _{2}}{v _{1}} = \frac{T _{2}}{T _{1}} = 4 = 2

, and the wavelength grows to

λ_{2} = 6 \times 2 = 12

cm.

JEE Main · 2020 · 03 Sep 2020 · Shift 1 · Single correct option

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