The diagram above shows the wire of a sonometer box set into resonance by a vibrating tuning fork of frequency f, when the wire is stretched by a tension T, the resonating length of the wire is I while the wavelength of the sound produced is \(\lambda\). Which of the following statements about the frequency of vibration of the wire is not correct?
Attached Figure / Diagram
A
proportional to the mass per unit length of the wire
B
equal to the frequency of the tuning fork
C
inversely proportional to the length of the wire
D
proportional to the sqare root of the tension
Verified Correct Answer: A.
Physical Principles & Numerical Solution
The frequency of a vibrating stretched string or wire depends on three factors (i) Length of string l, (ii) Tension T, and (iii) Mass per unit length M
F ∝ \(\frac{1}{\text{l}}\)\(\sqrt{\frac{\text{T}}{\text{M}}}\)
From the formula above, the frequency of vibration of the wire is not proportional to the mass per unit length of the wire.
Source: Myschool Past Questions Archive (Record #33920)