Question

A tuning fork generates sound waves with a frequency of 240 Hz. The waves travel in opposite directions along a hallway, are reflected by walls, and return. The hallway is 46.0 m long and the tuning fork is located 14.0 m from one end. What is the phase difference between the reflected waves(in degrees) when they meet at the tuning fork? The speed of sound in air is 343 m/s. [answer 68.2°] Pls show steps

Answer 1

Answer:

The phase difference between the reflected waves when they meet at the tuning fork is 159.29 rad.

Explanation:

Given that,

Frequency of sound wave = 240 Hz

Distance = 46.0 m

Distance of fork = 14 .0 m

We need to calculate the path difference

Using formula of path difference

$\Delta x=2(L_{2}-L_{1})$

Put the value into the formula

$\Delta x =2((46.0-14.0)-14.0)$

$\Delta x=36\ m$

We need to calculate the wavelength

Using formula of wavelength

$\lambda=\dfrac{v}{f}$

Put the value into the formula

$\lambda=\dfrac{343}{240}$

$\lambda=1.42\ m$

We need to calculate the phase difference

Using formula of the phase difference

$\phi=\dfrac{2\pi}{\lambda}\times \delta x$

Put the value into the formula

$\phi=\dfrac{2\pi}{1.42}\times36$

$\phi=159.29\ rad$

$\phi\approx 68.2^{\circ}$

Hence, The phase difference between the reflected waves when they meet at the tuning fork is 159.29 rad.