Question

A string is stretched between fixed points separated by $40cm$. It is observed to have consecutive resonant frequencies of $340Hz$ and $510Hz$. Then, find the speed of wave on the string.

• A. $144m/s$
• B. $128m/s$
• C. $170m/s$
• D. $136m/s$

Answer 1

The correct option is D $136m/s$

The harmonics of the wave of $n^{th}$ order are given by,
$f_n=\frac{nv}{2L}$

Assume that $340Hz$ and $510Hz$ are $n^{th}$ and $(n+1{)}^{th}$ order harmonics, as they were consecutive.

$\therefore 510-340=\frac{(n+1)v}{2L}-\frac{nv}{2L}=\frac{v}{2L}$
$\Rightarrow v=170\times 2L=170\times 2\times 0.4$
$\Rightarrow v=136m/s$