Question

What is the amplitude of sin ?

Answer 1

The amplitude of a sine wave is the maximum height of the wave above its central axis, which in the equation provided is 0.2 meters. Two waves with the same amplitude and a phase difference of 180° have a resultant amplitude of 0 because they cancel each other out.

Step-by-step explanation:

The amplitude of a sine wave, represented as A in the function y(x, t) = A sin(kx – ωt), is the maximum height of the wave above its central axis. In the equation given where the wave equation is y(x, t) = 0.2 m sin(6.28 m⁻¹x – 1.57 s⁻¹t), the amplitude is 0.2 meters. When two sinusoidal waves with the same amplitude A and a phase difference of 180°, the resultant amplitude is 0 because the waves cancel each other out.

Answer 2

You haven't provided a graph or equation so I will tell the simplified meaning of amplitude instead.

Amplitude, is basically a distance from midline/baseline to the maximum or minimum point.

For sine function, can be written as:

`\displaystyle \large{ y = A \sin(bx - c) + d}`

• A = amplitude
• b = period = 2π/b
• c = horizontal shift
• d = vertical shift

I am not able to provide an attachment for an easy view but I will try my best!

We know that amplitude or A is a distance from baseline/midline to the max-min point.

Let's see the example of equation:

`\displaystyle \large{y = 2 \sin x}`

Refer to the equation above:

• Amplitude = 2
• b = 1 and therefore, period = 2π/1 = 2π
• c = 0
• d = 0

Thus, the baseline or midline is y = 0 or x-axis.

You can also plot the graph on desmos, y = 2sinx and you will see that the sine graph has max points at 2 and min points at = -2. They are amplitude.

So to conclude or say this:

If Amplitude = A from y = Asin(x), then the range of function will always be -A ≤ y ≤ A and have max points at A; min points at -A.