What is Sine waves: Definition and 35 Discussions

A sine wave or sinusoid is a mathematical curve that describes a smooth periodic oscillation. A sine wave is a continuous wave. It is named after the function sine, of which it is the graph. It occurs often in both pure and applied mathematics, as well as physics, engineering, signal processing and many other fields. Its most basic form as a function of time (t) is:


A, amplitude, the peak deviation of the function from zero.
f, ordinary frequency, the number of oscillations (cycles) that occur each second of time.
ω = 2πf, angular frequency, the rate of change of the function argument in units of radians per second


{\displaystyle \varphi }
, phase, specifies (in radians) where in its cycle the oscillation is at t = 0. When


{\displaystyle \varphi }
is non-zero, the entire waveform appears to be shifted in time by the amount φ/ω seconds. A negative value represents a delay, and a positive value represents an advance.
The sine wave is important in physics because it retains its wave shape when added to another sine wave of the same frequency and arbitrary phase and magnitude. It is the only periodic waveform that has this property. This property leads to its importance in Fourier analysis and makes it acoustically unique.

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  1. T

    How to mechanically produce modified SINE wave motion

    Piston displacement as a function of time produces a sine wave. I need to modify the motion so the the time the piston spends at both the bottom of the stroke and the top of the stroke are extended. The motion curve would approximate a clipped audio wave. The attached image shows three motions...
  2. Q

    I Why is Photon Energy Quantized in Terms of Sine Wave Frequency?

    Hello everyone, I've been grappling with a concept for years, diving into internet resources and pestering professors, yet I still find myself tangled in confusion. I'm reaching out in hopes that someone here can shed light on a question that has been haunting my thoughts regarding the nature...
  3. J

    I Are electromagnetic waves sine waves?

    Light is said to consist of photons or electromagnetic waves. I'm not asking which view is correct, what conditions make one view or the other more useful, or advantages and disadvantages of each view. I am assuming the two views are compatible to the extent that the wave character of light can...
  4. T

    Photoelectric effect , Superposition of sine waves

    Homework Statement In a photoelectric effect experiment, a monochromatic plane wave of light falls on a metal plate. The electric field in the light wave at a point near the plate varies according to E=E_0 \cos (\omega t). This results in a saturation current of 6 μA. If instead, the light wave...
  5. T

    Why Does a Single Sine Wave Show Multiple Frequencies on a dB Graph?

    So I am just working with a synth and I am having it create a single sine wave. I am then looking at the output on a db vs frequency graph and I would expect the db to only be reading at the frequency of that sine wave, but there are readings from 20 Hz all the way to 2k Hz sometimes(althought...
  6. F

    How Do I Generate Quarter Sine Waves?

    Hello, I need to find out how to generate a standing sine wave, or a quarter sine wave. I had no trouble finding out how to create a full or half wave rectifier, but very little generating a quarter wave, & that info mostly dealt with sound waves. I am doing this for experimental purposes...
  7. S

    I Trigonometry - sine waves between objects

    Can you use any trigonometric wave to describe a phenomenon between two different objects? In the sense like a line or parabola would talk about a relation between two variable thanks so much in advance
  8. S

    What is the frequency of the sum of several sine waves?

    I am given three sine waves with individual frequency being 10 Hz, 50 Hz, and 100 Hz. What is the frequency of the following : y(t) = sin(2π10t) + sin(2π50t) + sin(2π100t) Is it simply 100, the LCM of all the sin waves? If not, How to calculate the frequency of y(t) ?
  9. N

    Follow-up question about my understanding on rectification

    I understand the process of rectification but just only in theory. But I still have questions that I guess will be answered if I can experience or has experience about it (but sadly I don't have). Please kindly answer these questions: 1. Does the waveform of Vout can be considered as DC (...
  10. N

    Are waves always the sum of sine waves?

    I saw that somewhere and it is supposed to be something Fourier came up with but I can't find somewhere why... Please explain (with mathematical description if possible)
  11. N

    Deriving the formula for sine waves

    Can anybody out there show me how the sine wave formula y=Acos(kx - ωt + φ_{0}) or y=Acos(kx + ωt + φ_{0}) is the direct solution of the wave equation \frac{\partial^2 y}{\partial t^2} = v^2 \frac{\partial^2 y}{\partial x^2} ? I mean I looked it over on the Internet but everybody keeps...
  12. S

    Create a Perfect Signal with Sine Wave Summation

    Hi I just wanted to check my approach. I have spectrum I have peak at 10Hz another at 20Hz and a third at 30Hz. The amplitudes are 1000, 500, 250. I want to recreate the signal by summing sine waves. I assume that I will therefore take A1 = 1; A2 = 0.5; A3 = 0.25; I will then let y =...
  13. B

    Group velocity of two superimposed sine waves

    Hi all, I understand the concept of group velocity when applied to superimposed sine waves of the same amplitude, and even when applied to wave packets (in which case you get the well-known expression ∂ω/∂k). My question is what happens when you add two sine waves of different amplitudes? So...
  14. Newtons Apple

    Understanding the Relationship Between Sine Waves and Sine Angles?

    Hello everyone. Can someone explain the relationship between the idea of a sine wave, and the idea of a sine angle? I'm getting into trig, and I hear both terms of sin tossed around, but they seem to be completely unrelated. What does the angle of the triangle have to do with a wave? Same...
  15. M

    Combining Sine Waves: Adding 2 sin (314.2t) and 2 sin(314.2t - 120°)

    I need to add together the following sine waves and express the answer in the same form: Va = 2 sin (314.2t) + Vb = 2 sin(314.2t - 120°) Any help would be greatly appreciated.
  16. N

    Use LabView to simulate 2 Sine Waves and then Filter Waves above 50Hz

    Homework Statement Create a VI that will: simulate two sine waves of different frequencies (run it for 20 and 12 0 Hz). Add the sine waves and plot the sum. Then use a filter to remove signals above 50 Hz, and plot the filtered resHomework Equations The Attempt at a Solution I have attached an...
  17. R

    Determining the possible time interval between two sine waves

    ok I just got stuck half way into a problem, I would like it if someone explained it! Ok the question says, two identical sinusodial waves with a wavelength of 3.0 m and traveling in the same direction with a v of 2m/s. Starting from the same point, just the second waves starts later. and the...
  18. E

    Arduino Sine Wave: Piezo Buzzer Possible?

    Is it possible for an Arduino to produce a sine wave to a piezoelectric buzzer?
  19. T

    Why do sine waves define pure frequency?

    Like the title says, I'm curious why sine waves are often referred to as "natural" or "pure" oscillations. Why not some other oscillating function? As an example of the type of idea I'm referring to, the wikipedia "Sine Wave" article says: To me, the argument that it sounds pure because...
  20. E

    Using rotating vector to draw sine waves

    We have met the idea that a radius of a circle rotating ANTI-CLOCKWISE can be used to draw a sine wave... I get that... it is a great idea but...why does it have to be rotating anti-clockwise. That seems so un natural to me. We were told it is a convention. Does that mean it is something...
  21. L

    Solving Sine Waves Problem: Find Time for π Radians

    A sine wave with a frequency of 10Hz and an amplitude of 5 units phases from zero to 2π radians in a complete cycle. How long does it take for the phase to reach a value of π radians? y(t) = A . sin (2.π.f.t + φ) 0.1 = 5 x sin (2x∏x10x time + 3.14) time = 0.038 seconds But the answer...
  22. R

    Calculate phase angle between sine waves?

    Hello, I am trying to work out how to determine the phase angle between two sine wave mathematically? I have setup a Matlab Simulink model and I would like to calculate the phase angle between my current and voltage (both at the same frequency) without using preprogrammed blocks, as i...
  23. S

    Calculating Peak-to-Peak Amplitude of Out-of-Phase Sine Waves

    Two sine waves have equal peak to peak amplitudes 81 but are out of phase by 90 degrees. What is the peak to peak amplitude of the resultant wave. I have no idea how to start this question, could someone give me guidance?
  24. M

    Comparing Sine Waves with PIC Microcontrollers

    hello i need to now if i can compare between two sine wave by pic 16f877A or pic 16f628A? that the input of pic become sine wave , can the pic read that wave or can generate it? how i can do this ? Any ideas?
  25. S

    Help Understanding Oscillators and Sine Waves

    Kind of new to this stuff, so hopefully you guys will bear with me. So a simple Oscillator with a Capacitor and Inductor... I understand that the energy flow causes the inductor to generate and collapse a magnetic field. I also understand that Sine waves are generated by changing the...
  26. T

    Sine waves and 4th derivative and 4 dimensional space-time relationship?

    The 4th derivative of a sine wave is itself. This, of course, not only is a fact, but can be used to define the sine wave. My question is, are there any theories relating the abundance of sine waves in QM to the fact that the largest dimensions of space-time are together 4 dimensional? For...
  27. E

    Calculate phase between sine waves given the time difference

    Homework Statement How do i find the phase between sine waves knowing the time difference between each? http://users.bigpond.net.au/exidez/sinewave.jpg Equation for the main function is 3cos(30t - Pi/2) The smaller sine wave is of the same frequency when is settles in a steady state...
  28. D

    Why Are Sine Waves a Function of (t-(x/v))?

    Hey friends and Sir's , I am trying to understand simple concept that why sine waves are function of (t-(x/v)) x= position in x direction v= velocity of wave t= is time at any instant although i have read many articles on it but still unable to understand , any help will be great and...
  29. A

    Electronics converting sine waves to current

    How are sine waves converted to current?? Im doing avionics in physics at the moment and we are talking about receivers... i now that the resonate oscilates at certain frequency and the antenna picks up the sine waves that are at the frequency... but how are they then turned into current...
  30. S

    Square waves sine waves etc(signal propagation)

    err probably skin too many q's but anyway... what type of waves are made from naturall sources?eg then sun etc...are theren any square waves...im just wandering ifn there's any weirdness or differences when using square waves as a carrier wave in transmitting...if u know any good info sources...
  31. M

    Rules governing the creation of complex waveforms through addition of sine waves

    I'm interested in synthesizing complex waveforms using sine waves. I know that when two sine waves which differ slightly in frequency from one another are summed, amplitude modulation (AKA "beating") with a frequency equal to the difference in frequency between the two sine waves ensues. This...
  32. C

    Sine Waves and Primes: Exploring the Connection Through Music

    Hi folks. I'm back to make a fool of myself again. It seems that I have a proof that the 'music' of the primes is caused by the interaction of a collection of sine waves. However, I have no idea whether this is old hat, trivial or interesting. Can somebody here tell me? PS. I don't know why...
  33. R

    Time difference between two sine waves

    "There are two sine waves having a phase difference of 20 degrees. After one reaches its maximum value, how much time will pass until the other reaches its maximum, assuming a frequency of 60 Hz." Should I go about this by assuming... sin(120pi*t) = sin(120pi(t + x) - 20) Any hints...
  34. I

    Sine Waves - Natural Emissions of All Matter?

    Are sine waves the waves that are theoretically deemed to be the waves [naturally] emitted by all matter? Or am I getting them confused with something else?
  35. F

    How can I simplify adding two sine waves using trigonometric identities?

    Add the following sine waves y= Asin(wt) + Bsin(wt + x) Where w=2(pi)f and x is a phase shift I SIMPLIFIED this for my friend using rotating vectors, then i got really annoyed realizing that I didn't know how to do it the direct way (trig identities). So I've posted it here for...