A progressive wave travelling along the positive x-direction is represented by $$y(x, t) = A\sin(kx - \omega t + \phi)$$. Its snapshot at t = 0 is given in the figure.

For this wave, the phase $$\phi$$ is:

Based on the wave equation and the provided snapshot at t = 0, the value of the phase constant $$\phi$$ is determined as follows:

1. Analysis of the Wave Equation

The general equation for the progressive wave is:

$$y(x, t) = A \sin(kx - \omega t + \phi)$$

At time t = 0, the equation simplifies to:

$$y(x, 0) = A \sin(kx + \phi)$$

2. Comparison with the Snapshot

According to the graph provided for $t = 0$, the wave starts from the origin and moves in the negative y-direction as x increases. This indicates that the graph represents a negative sine wave:

$$y = -A \sin(kx)$$

3. Solving for the Phase Constant ($$\phi$$)

To find $$\phi$$, we equate the two expressions for $$y(x, 0)$$:

$$A \sin(kx + \phi) = -A \sin(kx)$$

Using the trigonometric identity $$\sin(\theta + \pi) = -\sin \theta$$:

$$A \sin(kx + \phi) = A \sin(kx + \pi)$$

By comparing the arguments of the sine functions:

$$\phi = \pi$$

Conclusion:

The phase constant $\phi$ for the given wave snapshot is:

$$\boxed{\phi = \pi}$$