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 7 rad. At that instant, what is the phase at r=7m?

What is the phase at r = 9.5 m at the same instant?

Answer 1

The phase at r = 7.0 m is 3.5π rad, and the phase at r = 9.5 m is 4.75π rad.

Step-by-step explanation:

The phase of a spherical wave can be determined using the equation θ = k∙r, where θ is the phase, k is the wave number, and r is the distance from the origin. The wave number can be calculated using the formula k = 2π/λ, where k is the wave number and λ is the wavelength. In this case, the wavelength is 4.0 m, so the wave number is 2π/4.0.

Now, we can calculate the phase at r = 7.0 m. The phase can be determined using the formula θ = k∙r. Plugging in the values, θ = (2π/4.0)∙7.0 = 3.5π rad.

Similarly, we can calculate the phase at r = 9.5 m. θ = (2π/4.0)∙9.5 = 4.75π rad.