Exploring Sine Waves: Physical Shape vs. Graph Representation

In summary, a sine wave is a graph of oscillating particles as a function of time, but also represents the shape of a wave. It is called a sine wave because of both its physical shape and the sine function that represents it. The sine wave is a sine of a linear argument, such as sin(x - vt) which represents a wave with speed v. Its argument is linear in both x and t.
  • #1
san203
Gold Member
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Is Sine Wave just a graph of particles that do SHM? A wave on a string is also a Sine wave provided its particles are moving sinusoidally. But its shape also kind of represents a sine wave.
So is the wave on a string called a sine wave because of the physical shape that we can see or because of its Graph?
Or
What is a Sine Wave? Does it represent the shape of a Wave or is it just the graph of oscillating particles as a function of time?
 
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  • #2
hi san203! :smile:

it's both …

if you fix x, it's a sine function of t

if you fix t, it's a sine function of x​

a sine wave is a sine of a linear argument

for example, sin(x - vt) represents a wave with speed v,

and its argument is linear in both x and t
 
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1. What is a sine wave?

A sine wave is a mathematical curve that represents a periodic oscillation. It is a smooth, repetitive waveform that occurs naturally in many physical phenomena, such as sound, light, and electromagnetic waves.

2. How is a sine wave physically shaped?

A sine wave can be represented physically by a variety of phenomena, such as the motion of a pendulum, the vibrations of a guitar string, or the pattern of light and dark bands in a diffraction grating. It is characterized by a smooth, symmetrical curve with a peak and a trough, and a repeating pattern of oscillation.

3. How is a sine wave represented graphically?

In mathematics, a sine wave is represented graphically by a sinusoidal function. This function is a smooth, continuous curve that maps the values of the sine of an angle to points on a Cartesian coordinate system. The resulting graph resembles the shape of a wave, with the x-axis representing time and the y-axis representing amplitude.

4. What is the relationship between the physical shape and graph representation of a sine wave?

The physical shape and graph representation of a sine wave are closely related. The shape of the wave determines the values of the sine function, which in turn determines the points on the graph. The physical properties of the phenomenon producing the wave, such as amplitude and frequency, are reflected in the graph through changes in the height and period of the curve.

5. How is the amplitude and frequency of a sine wave related to its graph representation?

The amplitude and frequency of a sine wave are directly related to its graph representation. The amplitude corresponds to the height of the curve, while the frequency corresponds to the number of complete cycles of the wave per unit of time. Changes in the amplitude and frequency will result in changes to the shape and size of the wave on the graph.

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