In the given wave function, y = (7.6 m) sin (6.8x − 120t), we can extract the following quantities:
Amplitude: The amplitude of a sinusoidal wave represents the maximum displacement from the equilibrium position. In this case, the amplitude is given as 7.6 m.
Angular Frequency: The angular frequency (ω) represents the rate at which the wave oscillates in radians per second. It is related to the frequency (f) by the equation ω = 2πf. However, in the given wave function, the frequency is not explicitly provided. Instead, we have the coefficient of t, which is the angular frequency (ω). Therefore, the angular frequency is 120 rad/s.
Angular Wave Number: The angular wave number (k) represents the spatial frequency of the wave, indicating how rapidly the wave varies in space. It is given by the equation k = 2π/λ, where λ is the wavelength. In the given wave function, the coefficient of x is the angular wave number. Therefore, the angular wave number is 6.8 rad/m.
Wavelength: The wavelength (λ) represents the distance between two adjacent points on the wave that are in phase, such as two adjacent peaks or two adjacent troughs. It is inversely proportional to the angular wave number: λ = 2π/k. Using the angular wave number we obtained earlier, the wavelength is approximately 0.92 m (rounded to two decimal places).
To summarize: Amplitude: 7.6 m Angular Frequency: 120 rad/s Angular Wave Number: 6.8 rad/m Wavelength: Approximately 0.92 m