A wave has angular frequency 46.2rad/s and wavelength 3.57m. What is its wave number?
b).What is its wave speed?
a) wave number = 1/(wavelength)
= 0.280 m^-1
b) wave speed = (wavelength)*(frequency)
= (wavelength)*(angular freq.)/(2*pi)
= 26.25 m/s
To find the wave number of a wave, we can use the formula:
Wave number (k) = 2π / wavelength (λ)
Given:
Angular frequency (ω) = 46.2 rad/s
Wavelength (λ) = 3.57 m
To find the wave number, we can substitute the given values into the formula:
k = 2π / λ
k = 2π / 3.57
k ≈ 1.76 rad/m
So, the wave number of the wave is approximately 1.76 rad/m.
Now, let's move on to finding the wave speed.
The wave speed (v) of a wave can be calculated by the formula:
Wave speed (v) = angular frequency (ω) / wave number (k)
Given:
Angular frequency (ω) = 46.2 rad/s
Wave number (k) = 1.76 rad/m
Substituting these values into the formula, we can find the wave speed:
v = ω / k
v = 46.2 / 1.76
v ≈ 26.25 m/s
So, the wave speed of the wave is approximately 26.25 m/s.