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A spherical wave with a wavelength of 4.0 m is emitted from the origin. at one instant of time, the phase at r = 8.0 m is πrad. at that instant, what is the phase at r = 7.5 m ?

Respuesta :

Kalahira
Phase at r = 7.5 m is 3π/4 radians Since the distance between the 2 points is 8.0m - 7.5m = 0.5m and the total wavelength is 4.0m, that means that the specified point is 0.5m / 4.0m = 0.125 of a full wavelength behind in phase. One full wavelength is 2π radians, so the desired phase is lagging by 2π * 0.125 = π/4 radians. Therefore the phase at r = 7.5 m is π - π/4 = 3π/4 radians.

Answer:

phase of the wave at r = 7.5 m is given as

[tex]\Delta \phi = \frac{15}{16}\pi[/tex]

Explanation:

As we know the relation between phase difference and path difference is given by

[tex]\Delta \phi = \frac{2\pi}{\lambda}\Delta x[/tex]

now we know that phase of wave is 180 degree at a distance r = 8 m

so here we have

[tex]\pi = \frac{2\pi}{\lambda}(8m)[/tex]

[tex]\lambda = 16 m[/tex]

now we have to find the phase at r = 7.5 m

so again by above formula

[tex]\Delta \phi = \frac{2\pi}{16}(7.5)[/tex]

[tex]\Delta \phi = \frac{15}{16}\pi[/tex]

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