The given equation of the wave is:
?(?, ?) = 5.5sin(?(0.020? - 4.0?))
Comparing this equation to the standard form of a wave:
?(?, ?) = ?sin(?? - ω?)
We can determine the values for wavelength, frequency, amplitude, and speed using the following relationships:
Wavelength (λ) = 2π/k Frequency (f) = ω/2π Amplitude (A) = Absolute value of the coefficient of sin Speed (v) = λf
From the given equation, we can identify the following values:
A = 5.5 (Amplitude) k = π(0.020) (Wave number) ω = π(4.0) (Angular frequency)
Let's calculate the values:
Wavelength (λ) = 2π/k = 2π/(π(0.020)) = 100 cm Frequency (f) = ω/2π = (π(4.0))/(2π) = 2.0 Hz Amplitude (A) = 5.5 cm Speed (v) = λf = (100 cm)(2.0 Hz) = 200 cm/s
Therefore, the wavelength of the wave is 100 cm, the frequency is 2.0 Hz, the amplitude is 5.5 cm, and the speed of the wave is 200 cm/s.