Final answer:
- - The value of wave amplitude is 10.0 V/m
- - The value of frequency is 2x10⁶ Hz
- - The value of propagation velocity is approximately 100.2x10⁶ m/s
- - The value of wavelength is approximately 50.1 m
Step-by-step explanation:
To find the wave amplitude, frequency, propagation velocity, and wavelength of the given electric field, we can analyze the equation E(y,t) = 10.0 cos(4πx10⁶t - 0.1257y) a V/m.
-- Wave Amplitude:
The wave amplitude is the maximum value of the electric field, which can be determined from the given equation. In this case, the wave amplitude is 10.0 V/m.
-- Frequency:
The frequency of the wave can be calculated from the coefficient of t in the cosine function. In this case, the coefficient is 4πx10⁶. Since the general formula for angular frequency (ω) is ω = 2πf, where f represents frequency, we can rearrange the formula to solve for f:
4πx10⁶ = 2πf
f = (4πx10⁶) / (2π)
f = 2x10⁶ Hz
Therefore, the frequency of the wave is 2x10⁶ Hz.
-- Propagation Velocity:
The propagation velocity (v) of a wave in a medium is given by the formula v = λf, where λ represents the wavelength. In this case, we need to determine the wavelength in order to calculate the propagation velocity.
To find the wavelength, we need to analyze the coefficient of y in the cosine function. In this case, the coefficient is -0.1257. The wavelength (λ) can be calculated using the formula:
λ = (2π) / (-0.1257)
λ ≈ 50.1 m
Therefore, the wavelength of the wave is approximately 50.1 m.
Now, we can calculate the propagation velocity using the formula v = λf:
v = (50.1 m) x (2x10⁶ Hz)
v = 100.2x10⁶ m/s
Therefore, the propagation velocity of the wave is approximately 100.2x10⁶ m/s.