Question

A string is stretched between fixed points separated by $75.0cm$. It is observed to have resonant frequencies of $420Hz$ and $315Hz$. There are no other resonant frequencies between these two. The lowest resonant frequency for this string is

• A. $105Hz$
• B. $305Hz$
• C. $205Hz$
• D. $10.5Hz$

Answer 1

The correct option is A $105Hz$

Frequency : $f=\frac{v}{2L}n$, where $v$ is the velocity of sound, $n$ is an integer and $f$ is the frequency.
The highest common factor will be the fundamental frequency.
HCF of $420$ and $315$ is $105$.
Hence, the resonant frequency is $105Hz$.