Physics - Wave on String Question with Solution | TestHub

The relation between phase difference $\Delta \varphi$ and path difference $\Delta x$ is given by:

$\Delta \varphi =\frac{2\pi }{\lambda }\Delta x$

Substituting the given values, $\Delta \varphi =1.6\pi$ and $\Delta x=40\text{ cm}=0.4\text{ m}$:

$1.6\pi =\frac{2\pi }{\lambda }\times 0.4$

$1.6=\frac{0.8}{\lambda }$

$\lambda =\frac{0.8}{1.6}=0.5\text{ m}$

The relation between velocity $v$, frequency $f$, and wavelength $\lambda$ is:

$v=f\lambda$

Substituting $v=330\text{ m/s}$ and $\lambda =0.5\text{ m}$:

$330=f\times 0.5$

$f=\frac{330}{0.5}=660\text{ Hz}$

Answer: 660 Hz