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A uniform rope of length 12 m and 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 wave length 0.06 m is produced at the lower end .of the rope. What is the wavelength of the pulse when it reaches the top of the rope?

A uniform rope of length 12 m and 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 wave length 0.06 m is produced at the lower end .of the rope. What is the wavelength of the pulse when it reaches the top of the rope?

Grade:11

3 Answers

Aditi Chauhan
askIITians Faculty 396 Points
7 years ago
Hello Student,
Please find the answer to your question
KEY CONCEPT: The velocity of wave on the string is given by the formula
v = √T/m
Where t is the tension and m is the mass per unit length. Since the tension in the string will increase as we move up the string (as the string has mass), therefore the velocity of wave will also increase. (m is the same as the rope is uniform )
∴ v1/v2 = √T1/T2 = √2 x 9.8/8 x 9.8 = 1/2 ∴ v2 = 2v1
Since frequency remains the same
∴ ℷ2 = 2ℷ1 = 2 x 0.06 = 0.12 m

Thanks
Aditi Chauhan
askIITians Faculty
SHAIK AASIF AHAMED
askIITians Faculty 74 Points
7 years ago
Hello student,
vtop/vbottom=sqrt(ttop/tbottom)=sqrt(6+2/2)=2
So f\lambdatop/f\lambdabottom=2
as frequency is same we get\lambdatop=2(\lambdabottom)=2(0.06)=0.12
Thanks and Regards
Shaik Aasif
askIITians faculty
Yash Chourasiya
askIITians Faculty 256 Points
one year ago
Dear Student

As rope is heavy, Tension is different at different points.Tat lower end is2gand at upper end is6g
V=vλ
643-590_Untitled.png

I hope this answer will help you.
Thanks & Regards
Yash Chourasiya

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