Answer:
The phase difference is 0.659 rad.
Explanation:
Given that,
Distance between two identical loudspeakers d= 1.00 m
Distance between speakers and listener r= 4.00 m
Frequency = 300 Hz
Suppose we need to find the phase difference in radian between the waves from the speakers when they reach the observer
We need to calculate the r'
Using Pythagorean theorem
[tex]r'=\sqrt{d^2+r^2}[/tex]
Where, d = distance between two identical loudspeakers
r = distance between speakers and listener
Put the value into the formula
[tex]r'=\sqrt{(1.00)^2+(4.00)^2}[/tex]
[tex]r'=\sqrt{1.00+16.00}[/tex]
[tex]r'=4.12\ m[/tex]
We need to calculate the path difference
Using formula of path difference
[tex]|r'-r|=4.12-4.00[/tex]
[tex]|r'-r|=0.12\ m[/tex]
We need to calculate the wavelength
Using formula of wavelength
[tex]\lambda=\dfrac{v}{f}[/tex]
Where, v = speed of sound
f = frequency
Put the value into the formula
[tex]\lambda=\dfrac{343}{300}[/tex]
[tex]\lambda=1.143\ m[/tex]
We need to calculate the phase difference
Using formula of phase difference
[tex]\phi=\dfrac{2\pi\times|r'-r| }{\lambda}[/tex]
[tex]\phi=\dfrac{2\pi\times0.12}{1.143}[/tex]
[tex]\phi=0.659\ rad[/tex]
Hence, The phase difference is 0.659 rad.
