Q6 / 117 · NTA Abhyas (JEE Main) 2020 · Physics · Waves and Sound

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

  • Correct answer
    A
    144  cm
  • B
    204  cm
  • C
    288  cm
  • D
    72  cm

Solution

Let the vibration takes place in the nth mode

So, for 1st case, nλ2=L ......(i)

And for 2nd case, n+1λ′2=L .....(ii)

From Equations. (i) and (ii), we get

nλ2=(n+1)λ′2 ∵   λ2=18 cm andλ′2=16 cm

⇒   18n=n+116

⇒    n=8

So, minimum possible length l=nλ2

⇒    l=8×18=144 cm

Hence, the correct answer is option: 'A'.

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