The wave function with a time period of 2π seconds, initial phase of (π/3) and amplitude of 50 meter can be represented by which of the following relations? (z,t) = 50 sin(kz - t) + π/3 (z,t) = 50 sin(z - kt) +π/3 (z,t) = π/3 sin(z - t) + 50 (z,t) = π/3 sin(k - t) + 50

The wave function can be represented by the equation (z,t) = 50 sin(z - kt) + π/3.

Here's why:

1. The amplitude of the wave is given as 50 meters. This is the maximum displacement of a point on the wave from its equilibrium position. In the wave function, this is represented by the coefficient of the sine function.

2. The time period of the wave is given as 2π seconds. The time period is the time taken for one complete cycle of the wave. It is related to the angular frequency (k) of the wave by the relation k = 2π/T. Here, T = 2π, so k = 1.

3. The initial phase of the wave is given as π/3. This is the phase of the wave at t = 0 and z = 0. In the wave function, this is represented by the constant term added to the sine function.

4. The wave function is of the form (z,t) = A sin(kz - ωt + φ), where A is the amplitude, k is the wave number, ω is the angular frequency, and φ is the phase. Substituting the given values, we get (z,t) = 50 sin(z - t + π/3).

5. However, since k = 1 and ω = 1, the wave function simplifies to (z,t) = 50 sin(z - t) + π/3.

Therefore, the correct relation representing the wave function is (z,t) = 50 sin(z - t) + π/3.