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.
Then, the lowest resonant frequency for this string is :

• A. $1.05$Hz
• B. $1050$Hz
• C. $10.5$Hz
• D. $105$Hz

Answer 1

The correct option is D $105$Hz

Given, $\frac{nV}{2L}=315⟶\left(1\right)$

& $\frac{(n+1)V}{2L}=420⟶\left(2\right)$

equation (2) $-$ equation (1), we get

$\frac{(n+1)V}{2L}-\frac{nV}{2L}=420-315$

$\Rightarrow [\frac{V}{2L}=105H_3]\to$ Lowest possible resonant frequency

$\therefore$ Option (D) is correct.