# How do I define a sine wave?

• SimonHollas
In summary, the conversation discusses an apparatus that produces a sine wave graph and the need to define it as a formula. The formula is determined by finding the amplitude, period, and phase of the wave.

#### SimonHollas

Dear All,

I have an apparatus that produces a graph of results that looks to me like a sine wave (a half wave plate affecting the power throughput of a laser; it goes from maximum to minimum 4x throughout its 360º rotation). My problem is that I need to define this line as a formula but have no idea where to start. Any ideas, anyone?

You look at the amplitude A (maximum height) of the wave. You also find the period T on the x-axis and if the wave is out of phase, you find the distance d from the origin of how much it is out of phase in the direction of positive x. Then the equation is

$$y(x) = Asin \left(\frac{2\pi (x-d)}{T}\right)$$

Thanks, Quasar987!

## 1. What is a sine wave?

A sine wave is a mathematical curve that describes a smooth repetitive oscillation. It is defined by the function y = A sin(Bx + C), where A is the amplitude, B is the frequency, and C is the phase shift.

## 2. How do I graph a sine wave?

To graph a sine wave, plot points on a Cartesian plane using the x-axis for the values of Bx + C and the y-axis for the values of y calculated using the equation y = A sin(Bx + C). Then, connect the points with a smooth curve.

## 3. What are the properties of a sine wave?

The properties of a sine wave include amplitude, frequency, period, and phase shift. The amplitude determines the height of the wave, the frequency determines the number of cycles per unit time, the period is the duration of one cycle, and the phase shift is the horizontal translation of the wave.

## 4. How do I use a sine wave in real life?

Sine waves are used in many real-life applications, including electricity, sound, and light. For example, alternating current (AC) electricity follows a sine wave pattern, and sound waves are often represented by sine waves. Sine waves are also used in signal processing and communication systems.

## 5. Can a sine wave have a negative amplitude?

Yes, a sine wave can have a negative amplitude. The amplitude of a sine wave can be positive, negative, or zero, and it determines the height of the wave above or below the x-axis. A negative amplitude simply means that the wave is mirrored below the x-axis.

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