Waves

JEE Main level, single correct, medium

16 of 142

Question 16 of 142

A uniform thin rope of length 12m12m and mass 6kg6kg hangs vertically from a rigid support and a block of mass 2kg2kg is attached to its free end. A transverse short wave train of wavelength 6cm6cm is produced at the lower and the rope. What is the wavelength of the wave train (in cmcm ) when it reaches the top of the rope?

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Answer: (C) 1212

V=fλV=f\lambda
V1λ1=V2λ2\dfrac{{V}_{1}}{{\lambda }_{1}}=\dfrac{{V}_{2}}{{\lambda }_{2}}
λ2=V2V1λ1=T2T1λ1{\lambda }_{2}=\dfrac{{V}_{2}}{{V}_{1}}{\lambda }_{1}=\sqrt{\dfrac{{T}_{2}}{T1}}{\lambda }_{1}T2=8g(Top){T}_{2}=8g\left(Top\right)
8g2gλ1\sqrt{\dfrac{8g}{2g}}{\lambda }_{1}
T1=2g(Bottom){T}_{1}=2g\left(Bottom\right)=2λ1=12cm=2{\lambda }_{1}=12cm

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