Question

A $20cm$ long rubber string fixed at both ends obeys Hooke's law. Initially, when it is stretched to make its total length $24cm$, the lowest frequency of resonance is ${\nu }_0$. It is further stretched to make its total length $26cm$. The lowest frequency of resonance now will be

• A. the same as ${\nu }_0$
• B. greater than ${\nu }_0$
• C. lower than ${\nu }_0$
• D. None of these

Answer 1

Answer: (B)

Lowest frequency of resonance

$V_o=\frac{1}{2L}\sqrt{\frac{T}{\mu }}$

Let the tension when the total length became $24$cm be T

When the string is stretched to $26$cm the tension in the string increases.

As T increases, frequency increases.

Hence option (B) is correct.