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Question

The equation of a standing wave in a stretched string is given by y=5sin(πx3)cos(40πt), where x and y are in cm and t is in sec. The separation between two consecutive nodes is (in cm)

A
1.5
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B
3
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C
6
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D
4
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Solution

The correct option is B 3
Given that, equation of standing wave is
y=5sin(πx3)cos(40πt)

Comparing this with
y=2Asin(2πxλ)cos(2πtT)

we get, λ=6 cm ; T=120 sec

Position of a node on the string is given by x=nλ2, where n=0,1,2,3,4.....

Seperation between two consecutive nodes is given by
Δx=nλ2(n1)λ2=λ2

From the given data,
Δx=62=3 cm

Alternate method :

At the nodes, the value of x is such that y=0.
To make sin function zero,
πxn3=nπ
For n=0,x0=0 cm
For n=1,x1=3 cm
seperation between two consecutive nodes is Δx=|x1x0|=3 cm

Hence, option (b) is the correct answer.

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