Question

Calculate the fundamental frequency of a string stretched by a 1 kg weight if the length of the string is 0.4 m. Given that 5 m length of the wire weight 2 g. (Assume tension to be constant in the string and equal to the point attached to the weight)

• A. $\frac{125}{2}\sqrt{10}Hz$
• B. $\frac{125}{4}\sqrt{10}Hz$
• C. $125\sqrt{10}Hz$
• D. None of these

Answer 1

The correct option is A $\frac{125}{2}\sqrt{10}Hz$

Tension, $T=mg=1\times 10=10N$
Mass per unit length of the rope, $\mu =\frac{0.002}{5}=\frac{1}{2500}kg/m$
Wave velocity, $v=\sqrt{\frac{T}{\mu }}=50\sqrt{10}m/s$
Fundamental frequency, $f_0=\frac{v}{2l}=\frac{50\sqrt{10}}{2\times 0.4}=\frac{125}{2}\sqrt{10}Hz$