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?
Answer: 40 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/4⇒ λ=4L=120cm -
2nd harmonic (n = 2):
L= 3λ/4 ⇒ λ=4L/3 =4×30/3 =40cm
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