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Question

A string fixed at both ends has a standing wave mode for which the distances between adjacent nodes is 18 cm. For the next consecutive standing wave mode distances between adjacent nodes is 16 cm. The minimum possible length of the string is:

A
144 cm
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B
204 cm
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C
288 cm
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D
72 cm
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Solution

The correct option is B 144 cm
Let the vibration takes place is nth mode
So, for 1st case, nλ2=L....(i)
and for 2nd case, (n+1)λ2=L....(ii)
From Eqs. (i) and (ii), we get
nλ2=(n+1)λ2[λ2=18 cm and λ2=16 cm]
18n=(n+1)16
n=8
So, minimum possible length l=nλ2
l=8×18=144 cm

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