Question

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 ?What is the phase at r = 9 m at the same instant?

Answer 1

The phase at r = 7.5 m is π rad, the same as at r = 8.0 m. The phase at r = 9 m is 0 rad (equivalent to 2π rad), as it completes a full cycle.

Step-by-step explanation:

The phase of a spherical wave at a given radius r from the origin depends on the wavelength λ and the radial distance r. The phase difference Δφ between two points at different radii is given by the formula Δφ = 2π – r) Λ, where ” is the inner radius and is the outer radius. Given that the phase at r = 8.0 m is π rad, we can use this formula to find the phase at r = 7.5 m and r = 9 m.

For r = 7.5 m:

Δφ = 2π – 7.5 m)  = 2π = π  rad

Hence, the phase at r = 7.5 m is also π rad since the wave has not completed a full cycle between the two radii.

For r = 9 m:

Δφ = 2π = π rad

The phase at r = 9 m is therefore π + π = 2π rad, which is equivalent to 0 rad (since phase is typically considered modulo 2π).