A 30 cm long string with one end clamped and the other free to move transversely is vibrating in its second harmonic. The wavelength of the constituents travelling waves is? - IQ786

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A 30 cm long string with one end clamped and the other free to move transversely is vibrating in its second harmonic. The wavelength of the constituents travelling waves is?

A 30 cm long string with one end clamped and the other free to move transversely is vibrating in its second harmonic. The wavelength of the constituents travelling waves is?

10 cm

30 cm

40 cm

120 cm

Explanation

We are given:

A 30 cm long string
One end is clamped (fixed), and the other is free to move transversely
It is vibrating in its second harmonic

We are to find the wavelength of the constituent traveling waves

The allowed standing wave lengths are: L=(n−1/2) λ/2 ,for n=1,2,3,…

So:

1st harmonic (n = 1):
$L = λ \Rightarrow λ = 4 L = 120 cm$
2nd harmonic (n = 2):
$L = 3 λ/4 \Rightarrow λ = 4 L/3 = 4 \times 30 = 40 cm$