The vibrations of a string of length 20cm 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 C5 Given equation for string y=2sin(πx5)cos(12πt)
Comparing this with
y=2Asin(2πxλ)cos(2πtT) we get, λ=10cm
Position of a node on the string is given by x=nλ2 , where n=0,1,2,3..... From the given data, x=5n⇒x=0,5,10,15,20 So for a 20cm long string, 5 nodal points are formed.