WHICH OF THE FOLLOWING FUNCTIONS OF X AND T REPRESENTS A PROGRESSIVE WAVE ?

Options

A. Y=SIN (4T-3X)
B. `y = (1)/(4+(4T-3X)^(2)`
C. Y = `1/(4T+3X)`
D. 1/(4T+3X)`

Answer

To determine which of the given functions of \( x \) and \( t \) represents a progressive wave, we need to analyze the functions based on two main criteria:

### Step 1: Identify the Form of the Function
A progressive wave can typically be represented in the form:
\[ y(x, t) = A \sin(kx \pm \omega t) \]
or
\[ y(x, t) = A \cos(kx \pm \omega t) \]
where \( A \) is the amplitude, \( k \) is the wave number, and \( \omega \) is the angular frequency. The key point is that the relationship between \( x \) and \( t \) should be linear.