Physics - Wave on String Question with Solution | TestHub

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

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

Given $\Delta \varphi =45^{\circ }=\frac{\pi }{4}$ rad and $\Delta x=4.0$ m, we substitute these values into the formula:

$\frac{\pi }{4}=\frac{2\pi }{\lambda }\times 4.0$

$\lambda =8\times 4.0=32$ m

The velocity of the wave is given by:

$v=f\lambda$

Substituting $f=300$ Hz and $\lambda =32$ m:

$v=300\times 32=9600$ m/s

Converting to km/s:

$v=9.6$ km/s

Answer: 9.6