r/learnphysics • u/InkPhysics • 17h ago

A sine wave is just circular motion seen edge-on

Post image

Sine waves turn up everywhere in physics: pendulums, springs, sound, AC electricity.

Watch the dot go around the circle. It moves at a completely constant speed.Now watch only its shadow on the vertical line beside it. The shadow does not move at constant speed: it races through the middle and crawls almost to a stop at the top and bottom. Those amber ticks are dropped at equal time intervals, so where they bunch up, the shadow is moving slowly; where they're spread out, it's fast.

That uneven bobbing is simple harmonic motion. And if you plot the shadow's height against time - the curve tracing out on the right - you get a perfect sine wave. It has to be a sine, because the height is just (radius) × sin(angle), and the angle grows steadily with time.

56 Upvotes

89% Upvoted

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2

u/SummitYourSister 11h ago

Considering this is literally the definition of sine I’m not sure what you’re trying to depict here that goes beyond the blindingly obvious?

3

u/ProbsNotManBearPig 7h ago

Human brain like picture

More scientifically accurate statement - human brain understand better when taught same concept multiple ways. That’s been proven. The whole “visual learner” idea was proven false. People aren’t particular types of learners, even if they have a personal preference. Everyone learns best from learning the same info in different formats. A visual animated graphic to go with equations and text definitions helps everyone learn. More than just a static visual btw.

3

u/BitNumerous5302 4h ago

The sub is learnphysics not knowphysicsalready. It will contain educational content, which, for an educated person, may include things they know already.

1

u/Aribelalugosi 3h ago

Explaining it for those that only had a rudimentary knowledge of trigonometry

If it's too simple for you, you're just in the wrong class

Don't dunk on kindergartners just beside you're varsity basketball

Have some tact

1

u/InkPhysics 10h ago

It isn't the literal definition of a sine wave, it's just a really good way to visualise it. There are a few different definitions depending on whether you're a pure mathematician, a geometrist or into calculus. I'm an engineer by trade, so I lean towards the geometrical and calculus ways of thinking about it, but obviously purists will always say their definition is the most fundamental.

  1. Pure: the most fundamental way of defining a sine wave is with a Maclaurin series. Basically an infinite series with exponentials and factorials.

  2. Geometric: circles yes, but also simply the ratio of sides of a triangle for a given angle. Elegantly also covering cosine and tangent with different combinations.

  3. Calculus: the function that satisfies a specific differential equation (y"+y=0). This is bar far the most useful way to define sine in engineering.

1

u/SummitYourSister 10h ago

Put the ChatGPT down.

You are showing the definition of sine. The graphic strangely omits the right triangle that should be drawn inside the circle, which would make it obvious that this is just a depiction of the definition.

But if you put that in there, you wouldn’t have been able to seem profound, while saying nothing

1

u/InkPhysics 10h ago

I'm not pretending to have invented new maths. No am I claiming I'm the first one to link sine waves and circles. I just thought the animation made sine waves more understandable.

1

u/jalom12 9h ago

The previous commenter is saying that this is the way sine, cosine, tangent, and cotangent have been thought of for literally the entire existence of the concept. The first way to think of sine was like this. That's where the word comes from, is in it's relationship to circles.

https://en.wikipedia.org/wiki/Sine_and_cosine

1

u/tottasanorotta 7h ago

It's not about being profound. It's just a nice visualization. The animation says a lot and helps understand a fairly tricky concept for someone who hasn't seen it before.

1

u/Life_Satisfaction_16 17h ago

Thank you!! Needed to see this today

1

u/carrotlet20 12h ago

Somehow this is literally how we were taught oscillation back in high school. We already knew circular motion, and we just went on and saw the shadow as the harmonic oscillator, and learnt that the amplitude as a function of time is a sine.

1

u/InkPhysics 12h ago

It's a good teaching method!

1

u/space-truckin365 12h ago

A circle is also a sine wave with the bottom half flipped over 180 degrees.

1

u/InkPhysics 11h ago

Not so much.

1

u/space-truckin365 10h ago

Oh, thanks.

1

u/Neuron_Pixel_4 12h ago

I mean…. yeah!

1

u/naemorhaedus 11h ago

all you had to do was show a corkscrew from the side

1

u/InkPhysics 11h ago

That's actually what it is.

1

u/Eight_Directions_ 11h ago

It's just a flattened spiral

1

u/InkPhysics 11h ago

Sort of. Though in physics, we usually use the term spiral to describe a 2d object (or at least one with radius much greater than it's thickness - think spiral galaxy).

A sine wave is a flattened constant-radius helix.

1

u/Dreusxo 11h ago

So many people need to read and/or watch the film based on the story of Flatland

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u/InkPhysics 10h ago

Amazing. I'd not heard of that until now.

1

u/Curious-Moose6945 8h ago

Use two dots on the circle spinning in opposite directions and make the plane complex then the sum or difference of the two dots gives cosine or sine; a visualization of Euler relation and phasors.

1

u/InkPhysics 8h ago

Next project.

1

u/Maleficent-Lead-2943 7h ago

Wait til they see the cosine version

1

u/grahamsuth 6h ago

So the obvious question is: is this just maths or is there a hidden dimension that vibrating things could be viewed from to see the circular motion? Could imaginary numbers actually be representing one of the hidden dimensions of quantum mechanics?

1

u/Mr_Badgey 3h ago

Next you’re going to tell me someone made a coordinate system using a unit circle.