In the given wave equation y = 79 sin(2000t + 0.01x), we can identify the following parameters:
Amplitude: The amplitude of the wave is the maximum displacement of the wave from its equilibrium position. In this case, the amplitude is 79.
Frequency: The frequency of the wave represents the number of complete cycles the wave undergoes per unit of time. The frequency can be determined by looking at the coefficient of the "t" term within the sine function. In this case, the frequency is 2000 Hz.
Wavelength: The wavelength of the wave is the distance between two consecutive points on the wave that are in phase (e.g., two crests or two troughs). To calculate the wavelength, we need to compare the coefficient of the "x" term to the standard form of the wave equation. In this case, the coefficient of "x" is 0.01. The wavelength (λ) can be determined using the formula:
λ = 2π / k
Where k is the coefficient of "x." In this case, k is 0.01. Therefore:
λ = 2π / 0.01 ≈ 628.32 meters
Velocity: The velocity of the wave represents the speed at which the wave propagates through the medium. It can be calculated using the formula:
v = λf
Where v is the velocity, λ is the wavelength, and f is the frequency. Substituting the values we have:
v = (628.32 m)(2000 Hz) ≈ 1,256,640 m/s
Therefore, in the given wave equation y = 79 sin(2000t + 0.01x), the amplitude is 79, the frequency is 2000 Hz, the wavelength is approximately 628.32 meters, and the velocity is approximately 1,256,640 m/s.