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A string is fastened tightly between two walls 24cm apart. The wavelength of the second...

Physics
JAMB 2001

A string is fastened tightly between two walls 24cm apart. The wavelength of the second overtone is
  • A. 24cm
  • B. 16cm
  • C. 12cm
  • D. 8cm
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Correct Answer: Option B
Explanation
For a string fixed at both ends and plucked at the middle, the fundamental frequency is given
by f0 = v/λ, where v = velocity of sound, λ = wave length.
At its fundamental, note, the the length of the string is given l = λ/2, => λ0 = 2l, where λ0 = wave length fundamental note. for the first over tone, λ1 = l.
For the second over tone, λ2 = 21/3 = (2 x 24)/3 = 16cm.

i.e. λ2 = 16cm.

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