JEE PYQ: Waves And Sound Question 10
Question 10 - 2020 (03 Sep Shift 1)
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 the wavetrain (in cm) when it reaches the top of the rope?
(1) 3
(2) 6
(3) 12
(4) 9
Show Answer
Answer: (3)
Solution
Using, $V = f\lambda$
$\frac{V_1}{\lambda_1} = \frac{V_2}{\lambda_2} \Rightarrow \lambda_2 = \frac{V_2}{V_1}\lambda_1$
$T_2 = 8g$ (Top), $T_1 = 2g$ (Bottom)
Again using, $n = \frac{V}{\lambda} = \sqrt{\frac{T}{M}}\lambda_2 = \sqrt{\frac{T_2}{T_1}}\lambda_1$
$= \sqrt{\frac{8g}{2g}}\lambda_1 = 2\lambda_1 = 12$ cm
BETA
