Is a Sine Wave Defined by Its Physical Shape or Graph Representation?

[san203]

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?

 

[tiny-tim]

hi san203!

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