Question

a sound wave has a wavelength of 0.20m. what is the phase difference between two points on wire which are 0.65m apart

Answer 1

We can relate the wavelength $\lambda$ with the displacement difference between the points $\Delta x$ and the phase difference $\Delta \phi$ with the following equation:

$\lambda=\cfrac{2\pi \Delta x}{\Delta \phi} \implies \Delta \phi=\cfrac{2\pi \Delta x}{\lambda}$

We substitute and find the phase difference in radians:

$\Delta \phi=\cfrac{2\pi \Delta x}{\lambda}=\cfrac{2\pi (0.65\,m)}{0.20\,m}= 6.5\pi\,rad=1170^{\circ}$

In conclusion, the phase difference $\Delta \phi$ is 6.5$\pi$ radians or 1170°.

Reference:

• Sears, F. W., & Zemansky, M. W. (1973). University physics.