Answer:
The value is [tex]\Delta \phi = 4.12 \ rad[/tex]
Explanation:
From the question we are told that
The frequency of each sound is [tex]f_1 = f_2 = f = 540 \ Hz[/tex]
The speed of the sounds is [tex]v = 330 \ m/s[/tex]
The distance of the first source from the point considered is [tex]a = 4.40 \ m[/tex]
The distance of the second source from the point considered is [tex]b = 4.00 \ m[/tex]
Generally the phase angle made by the first sound wave at the considered point is mathematically represented as
[tex]\phi_a = 2 \pi [\frac{a}{\lambda} + ft][/tex]
Generally the phase angle made by the first sound wave at the considered point is mathematically represented as
[tex]\phi_b = 2 \pi [\frac{b}{\lambda} + ft][/tex]
Here b is the distance o f the first wave from the considered point
Gnerally the phase diffencence is mathematically represented as
[tex]\Delta \phi= \phi_a - \phi_b = 2 \pi [\frac{ a}{\lambda} + ft ] - 2 \pi [\frac{b}{\lambda} + ft ][/tex]
=> [tex]\Delta \phi = \frac{2\pi [ a - b]}{ \lambda }[/tex]
Gnerally the wavelength is mathematically represented as
[tex]\lambda = \frac{v}{f}[/tex]
=> [tex]\lambda = \frac{330}{540}[/tex]
=> [tex]\lambda = 0.611 \ m[/tex]
=> [tex]\Delta \phi = \frac{2* 3.142 [ 4.40 - 4.0 ]}{ 0.611 }[/tex]
=> [tex]\Delta \phi = 4.12 \ rad[/tex]
