What is Sine wave: Definition and 117 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. E

    B Sine wave noise at different frequencies

    Supposed your audio bandwidth is set to 20000Hz. And the signal is 10mV and there is spec of 2mV noise at 20000Hz bandwidth. Does it mean if a function generator would produce constant 10mV with different frequencies between 20Hz to 20000Hz. The noises in the sine waves of each would be similar...
  2. B

    I Equation to graph a sine wave that acts like a point on a unit circle

    I need an equation to graph a sine wave that act like a unit circle but only positive numbers. so I need it to be 0 at 0, A at 90 , 0 at 180, A at 270, 0 at 360, and A at 450 and so on and so on... Now I know sin(0) is 0 in degrees and sin(90) 1 and I know if you Square a number is...
  3. S

    I How Do You Calculate Day-Specific Phase Shifts in Excel for Sine Waves?

    Hi, I have created a sine wave with the following options: 1.) - changing the period/length in days of the sine wave (Cycle Length in Days) 2.) - calculating the start value of the "dummy" so that the sine wave always starts with -1 (Dummy Start at Cycle Trough) when the phase shift is set...
  4. J

    B RC Low Pass Circuit Sine Wave Response

    Hey Everyone, I am trying to gain a level of fundamental understanding of an RC circuit sine wave response through the mathematics and was wondering if someone could help me work it out. Fundamentally a sine wave is represented by the equation y=-ky'' . When a sine wave is used as the input...
  5. danieluyter

    What is causing the square drop in my guitar effect's sine wave?

    I built a guitar (fuzz) effect, and analysed the sine wave from a tone generator through an oscilloscope. Wondering what the wave means and how it got to be the way it is. I will attach a picture of the oscilloscope screen + the circuit I used for the Fuzz effect. My question is what the cause...
  6. arcTomato

    Engineering The power spectrum of a sine wave (C language)

    Hi I would like to Derive the power spectrum of sinusoid.I tried like this. But It doesn't work. <Moderator: CODE tags added> #include <stdio.h> #include <math.h> #define pi 3.1415926535 FILE *in_file, *out_file; int main() { dft(); } int dft(int argc, char *argv[]) { char...
  7. I

    A How can you generate a sine wave using integers only?

    I need to recursively generate a quadrature signal which fits exactly into a grid NxN, where N is a large power of two. After unsuccessful research, I decided to develop my own solution, starting from the waveguide-form oscillator taken from Pete Symons' book 'Digital wave generation, p. 100'...
  8. E

    Line voltage in 3 phase as single sine wave

    Howdy all. The typical image of a three phase electrical system involves 3 sine waves, phase shifted 120 degrees. These sine waves each, individually, represent the 'phase voltage,' which is to a common neutral in a wye configuration. In this wye configuration the line to line voltage is...
  9. V

    B How to set up an integral to integrate over a sine wave?

    How do I setup an integral to integrate over the following equation: V(t) = 1/(R*C) integral to t Vin(t) dt This is the capacitor voltage over time formula. I want to integrate over a sine wave from 9 to 81 degrees. Frequency of 120Hz, amplitude of 120V. The formula I used in wolframalpha is...
  10. Jason-Li

    Harmonic waves - Fundamental voltages

    Homework Statement An ac voltage, comprises of a fundamental voltage of 100 Vrms at a frequency of 120 Hz, a 3rd harmonic which is 20% of the fundamental, a 5th harmonic which is 10% of the fundamental and at a phase angle of 1.2 radians lagging. (i) Write down an expression for the voltage...
  11. A

    Modified sine wave vs pure sine wave inverter

    i was desigining a simple ( simple as in no MPPT) PV-pump standalone system, and we decided on using an AC-pump, so while i was searching for inverters i noticed the remarkable difference in price ranges, so i started to read about the difference between the two, so far the disadvantages of the...
  12. NickTheFill

    I Period of a Sine Wave: Understand How to Measure in Radians

    Dear all Something is bugging me. I hope you can help. I read in texts that if f(t) = sin(t) then the period of the function is the time taken (secs) to complete one cycle. I also read in texts that if f(t) = sin(2t) then the period of the halved. No problems here. I see that (2*t) = (omega*t)...
  13. L

    Generate sine wave with signal generator on scope

    I'm new to electronics, and using my new equiptment I would like to generate a sine signal on my function generator and display it on my oscilloscope. Equipment: * The scope is Rigol DS1054Z * Function generator is a $60 digital chinese. My problem is: When I plug connect the function...
  14. T

    B Simple double integration of square wave question

    Hi, Simple question, sort of: I see that according to the internet the mathematical description of a triangular wave is rather complex, so I'll try to stay as far away from that as I can, because I'm a bit rusty. I understand that if you integrate a square wave you get a triangular wave on the...
  15. Simoyd

    I How Do You Fit a Sine Wave to Data Points?

    So my question is, how does this work (hopefully I'm allowed to do hyperlinks): https://www.desmos.com/calculator/zlvrts7mul Given a table of x and y coordinates, how do I find the sin wave of best fit. I need to get f (frequency), a (amplitude), and p (phase) for the function in this form f(x)...
  16. 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...
  17. P

    Sine Wave Questions: Wavelength, Frequency, Speed

    Homework Statement A sinusoidal transverse wave traveling on a string is described at t=2.0s by y(x)=0.1sin(4πx+(33π/40) and at x=1.0m by y(t)=0.1sin((17π/4)+4πt) a. What is the wavelength and the amplitude? b. What is the frequency (Hz) and direction of propagation? c. What is the speed? d...
  18. F

    Engineering Circuit Analysis-Converting a square wave to a sine wave

    Homework Statement For an upcoming lab I've been asked to build a circuit to convert a square wave (vi(t))e into a sine wave (v0(t)) by selecting appropriate resistor/capacitor values for the circuit below (from what I know, it's impossible to produce an accurate sine wave with just this, I...
  19. A

    How Does Offset Impact RMS Voltage Calculation?

    Homework Statement The rms voltage for a sine wave with zero offset is given by Vrms= 1/(√2)Vpeak. Calculate the rms voltage for a sine wave with a peak-to-peak voltage of 1V. Homework Equations Vpeak-to-peak=2Vpeak The Attempt at a Solution This may be a really easy question with an answer...
  20. Tesladude

    Calculating Wattage with Sine Wave

    So my question is about calculating wattage with a sine wave. So with speakers I always just thought of it as the basic vi=w So a sine wave of 12v through 4 ohms will produce three amps and thus 36watts. But when you put a square wave and use pulse width modulation on something like an led or...
  21. CupOfAppleTea

    Intro Physics Books on Phase and Amplitude of a sine wave

    Hi! I am searching for litterature on the decomposition of a sine wave in its three parameters: phase, frequency and amplitude. I just need it to justify an analysis that I am doing this way and it appears to be hard to find such a book. I find many website but nothing I can cite seriously! Thanks!
  22. D

    Fourier Transform of a full rectified sine wave

    Homework Statement Derive the FT for a full-wave rectified sine wave, i.e., |sin(wt)| Homework Equations $$1/(√2π)\int_{a}^{b} |Sin[wt]| {e}^{-i w t}dt$$ The Attempt at a Solution I'm not entirely sure how to start doing this problem. What I tried doing was noticing that both of these...
  23. D

    Sine wave relationship with physical waves

    This is probably pretty basic but I've never actually seen an explanation of how exactly the sine wave relates to the physical waves it is so commonly used to represent. Could it be imagined as like the periodic thumping of a speaker where the peak of the sine graph represents maximum air...
  24. H

    Square wave and sine wave -- How standing waves are formed?

    Why do the sound waves reflect and form standing wave when they travel along a string with sinusoidal waveform? But they do not reflect back when they are in square waveform ?
  25. G

    Fundamental frequencies of square wave and sine wave

    Homework Statement What are the fundamental frequencies for a 50 kHz square waveform of 50% duty cycle and a 25 kHz sinusoidal waveform, respectively? (The duty cycle of a square waveform is the ratio between the pulse duration and the pulse period.) Homework Equations My teacher then gave...
  26. D

    ODE with base excitation caused by a half sine wave

    Homework Statement The suspension system of a car traveling on a bumpy road has a stiffness of ##k = 5\times 10^6## N/m and the effective mass of the car on the suspension is ##m = 750## kg. The road bumps can be considered to be periodic half sine waves with period ##\tau##. Determine the...
  27. P

    Calibrated sine wave generator

    Imagine that you have a calibrated sine wave generator set at 900 Hz and you mix its signal with that of an uncalibrated generator also set at 900 Hz. You hear a beat frequency of 4 Hz. What is the true frequency of the uncalibrated generator? Is there more than one possibility? I'm...
  28. E

    Dickey Fuller Test Sine Wave or seasonallity

    Hi can someone please clarify info regarding the application and validity of the Dickey Fuller test. If I perform the test using a sine wave would I be required to somehow take into account the seasonality. From my understanding a sine wave is non stationary, using the MATLAB command below I...
  29. Q

    Question about rms value of a sine wave

    Sorry if this sounds like a dumb question, but why is the effective value of a sine wave 0.707, as opposed to 0.637 which is the value generated by finding the definite integral over the domain [0,∏] divided length of the domain?
  30. O

    LM324: How to Create Sine Wave Output

    Hello i would like to know, how does LM324 create a sine wave after the output of the op amp?? thanks
  31. S

    MATLAB Measuring the 'purity' of a sine wave using FFT (Matlab)

    I have a range of sine waves I have obtained in an experiment. I want to put a measure on the purity of these sine waves - how well the reproduce a theoretical sine wave. Is there anyway I can analyse the FFT of the sine waves in Matlab and put a measure on the purity of the sine wave...
  32. A

    Sine wave power amplification question

    Hello all, I'm new to electrical engineering, and I'm working on a project that requires a bit more than I'm familiar with. What I'm asking for help on boils down to this: I have a circuit that outputs a low power sine wave (frequency 25-40kHz) with an amplitude +/- 5V at a few watts. I want to...
  33. T

    Java Sine wave equation into Java Code

    I have been trying to implement this Wave equation into java: A = amplitude of wave L = wave length w = spatial angular frequency s = speed wt = temporal angular frequency d = direction FI = initiatory phase Y(x,y,t)=A*cos(w *(x,y)+ wt*t + FI; I...
  34. A

    Can a half sine wave be inverted with a low-pass filter?

    I know that normal DC can be inverted to square wave , modified sine wave or pure sine wave , what about half sine wave dc , like the one resulted from ac current passing through a simple diode rectifier, can this be inverted?
  35. S

    Exploring Sine Waves: Physical Shape vs. Graph Representation

    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...
  36. N

    MHB Longitudinal excitation of a sine wave

    Hi! This is a problem regarding a quarter car model driving over a sinusoidal road excitation. A sinusoidal excitation can be written on the form ze^(jωt), z being vertical. I would like to write the longitudinal excitation of a sine wave on the same form? Any hints and tips are much appreciated.
  37. G

    Circuit Problem with diodes and resistors with sine wave input

    Homework Statement Sketch Vo for the network shown (see attachment) and determine the dc voltage available. Homework Equations The Attempt at a Solution Vi is a sine like wave with amplitude of 100 V and goes on for one period. When Vi is positive, the diode on the right goes...
  38. A

    Voltage, Current, and Time Graph with Sine Wave

    Homework Statement Hello all! Basically, my professor used this graph in our lecture, but I do not really understand how to read it. The graph has three variables, so I'm guessing it is Voltage vs. Current as time increases? One question he asked was "The figure shows the voltage and...
  39. O

    Converting Modifed Sine Wave to Sine Wave

    Good evening, I bought my self my first Inverter rated at 500W which has a peak rate of 1000W (1kW) maximum. Since some devices such as my main computer for one takes 600W, It does not like the modified sine wave. I was wondering if there is a way to somehow 'convert' the modified sine wave...
  40. 1

    Turn Envelope Wave into one Sine Wave

    Hello everyone, The sum of two sine waves that have close frequencies can produce an Envelope Wave: http://en.wikipedia.org/wiki/Envelope_(waves) What formula can I use to turn it into one wave (i.e. one frequency and amplitude)? Example pic attached: The blue "Envelope Wave" is...
  41. G

    Sine Wave between two Functions

    Just Thought this would be cool to share with yall So say you have two functions, B(x) and A(x) The equation \frac{b(x)+a(x) + (b(x)-a(x))sin(nx)}{2} Will give you a sin wave in between these two functions (I was playing around with this and finally figured out the equation a while ago). N...
  42. P

    What is the meaning of the y-axis on a sine wave graph?

    Okay this has been bothering me, I know what the x-axis on sine graph mean, but not the y axis. I know when I type for example: sin(pi) I will get 1. But what is that 1? I know its the y cordnate. But what is it?
  43. D

    What causes the oscillations in an RLC circuit?

    So I'm trying to get my head around RLC circuits and what is happening say we have a 10 ohm resistor, 1000uf capacitor and a 10H inductor in a circuit powered by a 10 volt source. Is the resulting oscillation of the sine wave frequency the result of the inductor resisting the flow of...
  44. dexterdev

    Why are there more zeros in a sine wave than 1s and -1s?

    Hello guys, From a layman's viewpoint when we count occurrences of different amplitude values, then frequency of zeros must be maximum is not it? but it is as below: why so? zeoros must be maximum, 1s and -1s are lesser than 0 isn't it?
  45. E

    How i can plot anti periodic sine wave in matlab ?

    i don't know how i can use MATLAB to plot anti periodic fun .. the origin site give this code for triangular fun: fs = 10000; t = -1:1/fs:1; x1 = tripuls(t,20e-3); plot(t,x1), xlabel('Time (sec)');ylabel('Amplitude'); title('Triangular Aperiodic Pulse') but when i use this for sine...
  46. Y

    Sine Wave measurements vs equations

    I have the equation E(t)=7*sin(11000t+∏/3) and I measured the following: E(.22ms) = .422V Frequency = 1.751kHz Period = 572.0 μs Peak = 7V Peak-Peak = 14V E(rms) = 4.8V E(average) = 105mV I've calculated the following to compare E(.22ms) = .422V Frequecy = 1.75 kHz Period...
  47. E

    Learn About Sine Wave Separation and Sound Processing

    Please forgive me, I don't really know how to properly ask my question, so I'll just do my best. I want to learn how sound is processed. More specifically what math goes into figuring out what individual frequencies are within a single sound signal. Like if I had a recording of say 5 separate...
  48. S

    Is Sqrt(3) Factor in 3-Phase Power Dependent on Sine Waves?

    The line current in a 3-phase delta loaded circuit is supposedly equal to sqrt(3) times the phase current. That's dependent on all the signals being sine waves though right? Because the math that gets you to that point is dependent on sine and cosine identities that don't necessarily hold with...
  49. dexterdev

    Why sine wave is the basic building block signal to make other signals?

    Why sine wave is the basic building block signal to make other signals? Not any other wave. -Devanand T