The equation y=5sin(3x-4)where y is in millimeters x is in metres and t is in seconds,represents a wave motion

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To determine whether the equation represents a wave motion, we need to analyze its components and characteristics.

First, let's look at the equation: y = 5sin(3x - 4).

1. Presence of a sine function: The equation contains the sine function, sin(3x - 4). The sine function is commonly used to describe oscillatory or wave-like behavior.

2. Coefficient of x: The coefficient of x is 3 in this equation. This indicates that the wavelength of the wave is related to the x-values. Since x is in meters, the wave's wavelength will be measured in meters as well.

3. Amplitude: The amplitude of the wave is given as 5. The amplitude represents the maximum displacement of the wave from its equilibrium position. In this case, the maximum displacement of the wave is 5 millimeters.

4. Phase shift: The presence of the term -4 within the sine function represents a phase shift. In this equation, it indicates that the wave is shifted 4 units to the right along the x-axis.

Based on these characteristics and components, we can conclude that the equation y = 5sin(3x - 4) represents a wave motion, where y is measured in millimeters, x is measured in meters, and it is assumed that t represents time.

To visualize the wave, you can plot the equation on a graph by assigning different x-values and calculating the corresponding y-values. This will give you a wave-like pattern that repeats over the x-axis.