Question

Two stretched strings have lengths l and 2l while tension are T and 4T respectively. If they are made of same material the ratio of their frequency is:

• A. 2 : 1
• B. 1 : 2
• C. 1 : 1
• D. 1 : 4

Answer 1

Answer: (C)

1 : 1

Frequency is given by
$v=\frac{1}{2l}\sqrt{\frac{T}{\mu }}$
$\therefore$ First frequency $v_1=\frac{1}{2l}\sqrt{\frac{T}{\mu }}$
and second frequency $v_2=\frac{1}{4l}\sqrt{\frac{4T}{\mu }}$
$\therefore$ hence, the ratio of frequencies $\frac{v_1}{v_2}=1:1$