Question

If the vibrations of a string are to be increased by a factor of two, the tension in the string should be made

• A. twice
• B. four times
• C. eight rimes
• D. half

Answer 1

Answer: (B)

The frequency of vibration of a string is given by $n=\frac{1}{2l}\sqrt{\frac{T}{m}}$ where $l$ is length, T the tension and m the mass per unit length. Given, $n_1=n,n_2=2n$ $\therefore$ $\frac{n_1}{n_2}=\frac{n}{2n}=\sqrt{\frac{T_1}{T_2}}$ $\Rightarrow$ $\frac{1}{4}=\frac{T_1}{T_2}$ $\Rightarrow$ $T_2=4T_1$ Hence, to increase n by a factor of 2 tension must increase four times.