**Distance travelled by a progressive wave in 5 seconds**

To determine the distance travelled by the wave in 5 seconds, we need to understand the equation provided and how it relates to the motion of the wave.

**Understanding the equation**

The equation given is in the form y = A sin(ωt - kx), where:

- y represents the displacement of the wave
- A represents the amplitude of the wave
- ω represents the angular frequency of the wave
- t represents time
- k represents the wave number
- x represents the position along the x-axis

In the given equation, y = 3 sin π(t/2 - x/4), we can identify the following values:

- A = 3 (amplitude)
- ω = π (angular frequency)
- t/2 - x/4 (argument of the sine function)

**Finding the wave number**

The wave number (k) can be determined by comparing the given equation with the standard equation form. In this case, k = 1/4.

**Calculating the distance travelled**

To calculate the distance travelled by the wave in 5 seconds, we need to determine the relationship between time and distance in the equation.

The equation shows that the displacement of the wave (y) depends on both time (t) and position (x). However, the given equation does not explicitly provide the relationship between time and distance.

To establish the relationship, we can consider the wave speed. The wave speed (v) is given by the formula v = ω/k. In this case, v = π/(1/4) = 4π.

The wave speed represents the distance travelled by the wave in one second. Therefore, in 5 seconds, the wave would travel a distance equal to 5 times the wave speed.

Hence, the distance travelled by the wave in 5 seconds is 5 * 4π = 20π metres.

**Conclusion**

The wave described by the equation y = 3 sin π(t/2 - x/4) travels a distance of 20π metres in 5 seconds. The distance travelled can be calculated by considering the wave speed and multiplying it by the time duration.

As general eqn of wave is Y=asin(wt-kx) By comparison w (omega) =1/2And K =1/4 And there is a formula k=w/vAfter substituting the value v=2 mNow we know speed of wave and time v =d/td=vt therefore answer is 10mHope that this should be right method..