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

Correct Answer:

Option B – 16cm

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.