A standing wave has wavenumber 200 rad/m. What is the distance between two adjacent nodes.
k = 2 pi / L = 200
L = 2 pi/200
distance between nodes of standing wave is half a wavelength L/2 = pi/200
To find the distance between two adjacent nodes in a standing wave, we need to identify the wave's wavelength first. The wavelength (λ) and wavenumber (k) of a wave are related by the formula:
λ = 2π/k
Given that the wavenumber (k) is 200 rad/m, we can now calculate the wavelength (λ):
λ = 2π / 200 = 0.0314 m (rounded to four decimal places)
In a standing wave, the distance between two adjacent nodes is equal to half of the wavelength. Therefore, we can find the distance between two adjacent nodes by dividing the wavelength by 2:
Distance between adjacent nodes = 0.0314 m / 2 = 0.0157 m (rounded to four decimal places)
So, the distance between two adjacent nodes in this standing wave is approximately 0.0157 meters.