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
[tex]\Delta x=2(L_{2}-L_{1})[/tex]
Put the value into the formula
[tex]\Delta x =2((46.0-14.0)-14.0)[/tex]
[tex]\Delta x=36\ m[/tex]
We need to calculate the wavelength
Using formula of wavelength
[tex]\lambda=\dfrac{v}{f}[/tex]
Put the value into the formula
[tex]\lambda=\dfrac{343}{240}[/tex]
[tex]\lambda=1.42\ m[/tex]
We need to calculate the phase difference
Using formula of the phase difference
[tex]\phi=\dfrac{2\pi}{\lambda}\times \delta x[/tex]
Put the value into the formula
[tex]\phi=\dfrac{2\pi}{1.42}\times36[/tex]
[tex]\phi=159.29\ rad[/tex]
[tex]\phi\approx 68.2^{\circ}[/tex]
Hence, The phase difference between the reflected waves when they meet at the tuning fork is 159.29 rad.
