Final answer:
The wavelength, frequency, period, and phase constant of the wave are approximately 38.55 meters, 75.96 Hz, 0.01317 seconds, and 5.03 radians, respectively.
Step-by-step explanation:
The transverse displacement (y) of a wave is given by the expression y(x,t)=y₍ sin(0.163x+5.03+477t). To find the wavelength, frequency, period, and phase constant, we first identify the wave number (k) and angular frequency (ω) from the equation, which are given by the coefficients of x and t, respectively. Here, k=0.163 m-1 and ω=477 s-1.
The wavelength (λ) can be found using the formula λ=2π/k. Subsequently, λ=2π/0.163 m, which calculates to approximately 38.55 meters.
The frequency (f) is obtained from ω using f=ω/2π. Therefore, f=477/2π s-1, which is approximately 75.96 Hz.
Once we have the frequency, the period (T) can be found using T=1/f. This gives T=1/75.96 seconds, which calculates to approximately 0.01317 seconds.
The phase constant (φ0) is the constant term in the wave function, which in this case is φ0=5.03 radians.