Question

A string fastened at both ends has successive resonances with wavelengths of $0.54m$ for the $n^{th}$ harmonic and $0.48m$ for the $(n+1{)}^{th}$ harmonic. The wavelength of the fundamental frequency is $432\times {10}^{-x}m$. What is the value of $x$?

• A. $1$
  
• B. $2$
  
• C. $3$
  
• D. $7$
  

Answer 1

The correct option is B $2$

For $n^{th}$ harmonic for string taut at two ends, $l=\frac{n\lambda }{2}$

Thus $\lambda \propto \frac{1}{n}$

Thus $\frac{n+1}{n}=\frac{0.54}{0.48}$

$⟹n=8$

$⟹l=\frac{8\times 0.54}{2}=2.16m$

When in fundamental frequency, $l=\frac{\lambda }{2}$

$⟹\lambda =4.32m$