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Question

The vibrations of a string of length 20 cm fixed at both ends are represented by the equation y=2sin(πx5)cos(12πt), where x and y are in cm and t in sec. How many nodes are located along the string?

A
3
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B
4
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C
5
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D
6
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Solution

The correct option is C 5
Given equation for string
y=2sin(πx5)cos(12πt)

Comparing this with

y=2Asin(2πxλ)cos(2πtT)
we get, λ=10 cm

Position of a node on the string is given by x=nλ2 , where n=0,1,2,3.....
From the given data,
x=5nx=0,5,10,15,20
So for a 20 cm long string, 5 nodal points are formed.

Thus, option (c) is the correct answer.

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