What is Sinusoidal: Definition and 229 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:

where:

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




φ


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



φ


{\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.

View More On Wikipedia.org
Recent contents Top users
  1. D

    The wave form of a sinusoidal current passing through a circuit?

    Assume a sinusoidal current I = I0sinωt passes through the circuit of: [PLAIN]http://a.yfrog.com/img52/9062/image2c1.jpg Obtain expressions for VC and VL in terms of ω and I0. Sketch the waveform for I, VC and VL, to show the phase relationship between these three variables. (Show about...
  2. I

    Solving Simple Harmonic Motion: Oscillatory & Sinusoidal in Time

    Hi, I having trouble grasping what: "oscillatory motions are sinusoidal in time" means... does this just mean that when solving a problem for simple harmonic motion that the equation is going to involve both and sin/cos and time? Sorry this might be more of a mathematical question.
  3. M

    Explaining Sinusoidal Motion: x = A sin(wt)

    Can someone please explain the following equation: x = A sin(wt) where A = amplitude, w = angular velocity, t = time. The way it's explained in my textbook is very confusing.
  4. X

    Calculating Phase Difference and Zero Point of Two Sinusoidal Waves

    Homework Statement Two sinusoidal waves in a string are defined by the functions y1 = (2.00 cm) sin(20.0x – 32.0t) and y2 = (2.00 cm) sin(25.0x – 40.0t) where y and x are in centimeters and t is in seconds. (a) What is the phase difference between these two waves at the point x...
  5. L

    Investigating Energy Conservation with Sinusoidal Waves

    Hi there. I am having trouble finding an explanation with waves. Suppose that you have to sinusoidal waves y1=Asin(kx-wt) and y2=Asin(kx-wt+phi) If we add them up, the resulting wave will be y=2Acos(phi/2)sin(kx-wt+phi/2). Now, if phi equals pi then the resulting wave will have no...
  6. D

    Max dynamic factor for sinusoidal load

    i posted it in general physics and got not answer. maybe this is the right place for this. thanks here is a question for max dynamic factor for sinusoidal load F*sin(at). say the natural frequency is b for a mass. then the max DLF considering damping is DLF=1/(1-(a/b)^2) when a>>b...
  7. N

    Deriving the displacement equation for a sinusoidal wave

    Hi everyone, I'm trying to understand the derivation of D(x,t) = A \sin{(kx - \omega t + \phi_o)} which is the displacement equation for a sinusoidal wave. The way my textbook (Physics for scientists and engineers by Knight) does it: Look at the graph of displacement versus position at time...
  8. N

    Sinusoidal Waves: Why Is Textbook Answer 1.5ym?

    The question and attempt to solution is on the attached image. I don't understand why the answer in the textbook is 1.5ym mine is 1.8 ym
  9. G

    Sinusoidal Wave traveling on a Composite String

    Cosider a sinusoidal wave traveling along a composite string. The string is under constant tension, F, and consists of a light portion (x<0) with mass per unit length mu1 joined in a continuous manner to a heavier portion (x>0) with mass per unit length mu2. Let y_1i(x,t)=A_1i*sin(wt-k_1x) be...
  10. G

    Sinusoidal wave traveling along a composite string

    I've been working on this one for quite some time... Consider a sinusoidal wave traveling along a string composed of two sections, one with a lighter mass/length density than the other. A pulse is traveling in the light region and about to hit the junction. If the incident wave is given by...
  11. 1

    Alternating (sinusoidal) Magnetic Field

    Homework Statement Imagine that a coil consisting of 75 turns of wire shaped as a circular loop with a radius of 12 cm is placed with its face perpendicular to the direction of an alternating (sinusoidal) magnetic field whose frequency is 60 Hz and whose maximum magnitude is 0.13 T (40...
  12. D

    Calculating Peak Displacement of Sinusoidal Motion

    I am looking at sinusoidal motion (shaker tables) and am trying to calculate peak displacement given RMS acceleration. I can easily find the peak displacement using: a_{pk} = 4\pi^2f^2x_{pk} a_{rms} = 0.707a_{pk} as... x_{pk} = \frac{a_{rms}}{0.707\pi^2f^24} My...
  13. S

    A sine curve coiled in a sinusoidal fashion?

    Ａ sine curve coiled in a sinusoidal fashion? Hi all, I am find the mathematical representation of a wire itself is of a sinusoidal shape, and now we coil this sinusoidal shaped wire into a sinusoidal shape again, so it's like a double sine wave. I have a rough idea, that is to first define a...
  14. stripes

    Applying a sinusoidal function to tidal patterns on the earth.

    Homework Statement At the time of a full moon, the tides repeat with a period of about 12 hours, and the depth of water in a certain channel varies between 2 meters and 6 meters in a way that can be modeled by an equation of the form D(t) = A + Bsin(ct + d), where A is the average depth and...
  15. G

    Does sinusoidal play a role in physics?

    Does sinusoidal motion play a special role in physics? Or is it just a mathematical intermediate step or auxiliary? For example of course you can Fourier transform any function, but you might as well chose not to do so and use the normal local differential equation. This way you never...
  16. B

    Sinusoidal Sound Wave Function

    Homework Statement A sinusoidal sound wave is described by the displacement wave function s(x,t)=(2.00 μm)cos⁡[(15.7 m^(-1) )x-(858 s^(-1) )t] b) Determine the instantaneous displacement from equilibrium of the elements of air at the position x = 0.050 m at t = 3.00 ms Homework...
  17. C

    Modeling Satellite Orbit with Sinusoidal Functions

    Homework Statement A satellite is deployed from a space shuttle into an orbit which goes alternately north and south of the equator. Its distance from the equator over time can be approximated by a sine wave. It reaches 4500 km, its farthest point north of the equator, 15 minutes after the...
  18. M

    Matlab function (M-File) that will create & play a sinusoidal waveform

    I am trying to create a MATLAB function (M-File) that will create & play a sinusoidal waveform with the given amplitude (A), frequency (f), sampling rate (Fs), and time span (tspan). the function must produce a .wav file with a specified filename. the MATLAB Function Format must be...
  19. H_man

    Freq response of forced sinusoidal motion:

    The book I am currently reading derives the response of an electron to an applied sinusoidal field as: 1/[1 + 2i (w - wa)/g] = 1 / (1 + i delta) where w and wa are the induced and resonance response frequencies and g the damping constant. And delta = 2 (w - wa)/g Up to this...
  20. L

    Solving ODE for Sinusoidal Voltage: Current i in Terms of Parameters and t

    setting a sinusoidal voltage term, the ODE can be written as (d^2 i)/(d t^2 ) + 25i = A0 sin (ϖt) assuming that ϖ^2 ≠ 25, determine the current i in terms of the parameters (ϖ and A0) and the variable t when the initial conditions are i(0) = di/dt (0) = 0 i really don't have much of...
  21. B

    Metal Heat Treatment: How to create a sinusoidal function that increases in frequency

    Alright, this is a hypothetical problem for my math class, (but it seemed to fit here better than calculus help) and though I am allowed to site sources, I don't necessarily want the answer just given to me (I mean, I'd really like to figure it out). Homework Statement Treatment lasts...
  22. P

    What really is a sinusoidal wave current (AC)?

    What really is a sinusoidal wave current? What exactly is happening to the electrons that is different from a DC? Are there any readings you suggest that will give me more insight into this? Thanks in advance.
  23. D

    Exploring the Effect of Large δ on Sinusoidal Function at x=1.5

    In a sinusoidal function...suppose the value of δ is very large...then as x approaches any a, the value of f(x) might not approach L directly...or there should not be a direct relation; example - \lim_{x \to 1.5} sin x = 0.997494986 Where I've stated δ as 7...then if x = 1.5 – 6.9 =...
  24. T

    Proof of sinusoidal periodicity

    Homework Statement Prove that f\left(x\right) = \cos(x) + \cos\left(\alpha x \right) where alpha is a rational number, is a periodic function. EDIT: Also, what is it's period? Homework Equations f\left(x\right + p) = f\left(x\right) trig identities The Attempt at a Solution First, I used...
  25. U

    Sinusoidal waveform issue

    I was routinely checking a question in an Engineering Maths book as listed below: The instantaneous value of voltage in an a.c. circuit at any time t seconds is given by v = 100 sin(50\pit - 0.523) V. Find: (a) the peak-to-peak voltage, the periodic time, the frequency and the phase angle...
  26. E

    Car Suspension, sinusoidal road input

    Homework Statement The question extends more than this but this is where I have difficulty. An uneven road surface is modeled by a sinusoid with amplitude 25mm and the car is driven at 100km/hr. Use the bode plot calculate earlier to obtain and explain the steady state force response when...
  27. N

    Average power of sinusoidal signal

    Homework Statement Question: Consider the sinusoidal signal: A*cos(\omegat + \phi) Determine the average power Homework Equations This is my first real attempt in signals and I am really confused with the question... I guess my question would be am I suppose to take the P = lim as t->...
  28. M

    Graph of a sinusoidal wave at a fixed position

    Homework Statement A sound wave is described by D(y,t) = (0.02mm)sin[(8.96 rad/m)y + (3140 rad/s)t + pi/4 rad)], where y is in metres, and t is in seconds. Draw a displacement-versus-time graph D(y=1.00m,t) at y= 1.00 m from t= 0 s and t= 4 ms. Homework Equations D(y,t) = (0.02mm)sin[(8.96...
  29. K

    Two sinusoidal waves of the same period

    Two sinusoidal waves, identical except for phase, travel in the same direction along a string and interfere to produce a resultant wave given by y(x,t)=(2.5 mm)sin(26.0x -4.0 s-1 * t+0.400 rad), with x in meters and t in seconds. 1.) What is the wavelength of the two waves (m)? [I...
  30. R

    Wevelength of sinusoidal wave generated by oscillator

    A sinusoidal wave is traveling along a rope. The oscillator that generates the wave completes 40.0 vibrations in 30.0 s. Also, a given maximum travels 425 cm along the rope in 10.0 s. What is the wavelength?
  31. D

    Sinusoidal Functions: Max/Min Volts in 1s w/ t-Values

    Homework Statement The voltage, V(t), in volts, of a power supply can be modeled by the function V(t) = 110sin5t+15, where t is the time, in seconds. Find the maximum and minimum voltages, within the first second, and the times they occur. Homework Equations The Attempt at a...
  32. B

    Sinusoidal voltage applied to zero resistance conductor

    Hi Guys, :smile: The following query would sound a bit ridiculous and abstract but it suddenly popped up in my head. :tongue: What would happen if I were to apply a purely sinusoidal AC voltage across a zero resistance conductor (theoretically, a super conductor) ? Zero resistance would...
  33. D

    Deriving RMS value from sinusoidal waveform.

    I'm having a problem with that integration part. The average value of i^2 in one cycle = (sum of all i^2 in that period)/(that period). To derive (sum of all i^2 in that period) we use integration, but that gives the area, how can the area be a substitution for this?...they are different...
  34. S

    Very basic - sinusoidal motion question

    I'm trying to work out the displacement of an object, knowing the acceleration, frequency and mass. I've found equations for working it out with the first two, but does the mass have an affect that should be taken into account? This is something very obvious that I will have only been taught...
  35. J

    Understand Sinusoidal Waves: Problem Solving

    Problem understanding waves. I can see how rates of speed in circular motion can translate to expressed different kinds/shapes of waves but I don' see why concepts of trigonometry like sin,cos are brought into describing waves. I just feel there could be clearer ways of describing waves.
  36. P

    How Do You Calculate Gain in Sinusoidal Signals?

    how does one calculate a gain in signal e.g sine wave. do we take peak-to-peak (or peak) of the output divided by peak-to-peak(or peak) of the input?
  37. H

    How Do Phase Shifts Affect Resultant Wave Amplitude and Frequency?

    Homework Statement Two traveling sinusoidal waves are described by the wave functions y1 = (5.00m) sin[pie(4.00x - 1 200t)] y2 = (5.00m) sin[pie(4.00x - 1 200t -0.250y)] where x, y1, and y2 are in meters and t is in seconds. (a) What s the amplitude of the resultant wave? (b) What is the...
  38. W

    Transverse Sinusoidal Wave Function

    A transverse sinusoidal wave on a string has a period of 25 ms and travels in the negative x direction with a speed of 30 m/s. At t=0, a particle on the string at x=0 has a displacement of 2 cm and is traveling downward with a speed of 2 m/s. Find the amplitude, phase constant, and maximum...
  39. F

    Sinusoidal waves and Maxwell eqns

    hello!, question about Maxwell equations: a linear restoring force causes simple harmonic motion. In Maxwell equations, what is this restoring force due to? In mechanics to mass and stiffness. do self inductance and capacitance the inertia and the stiffness? HElmholtz eqn resembles the...
  40. S

    Exploring the Relationship Between Bicycle Pedals and Sinusoidal Force

    Hi, I'm new to the forum so I hope this is the right place to post this, I actually joined to ask this question. I found something in the archive through a google search. The thread can be found at: https://www.physicsforums.com/archive/index.php/t-117265.html Some of the things in there were...
  41. A

    Why is the electric potential equation incorrect in this paper?

    In a paper I am reading it states that since the electric potential (and field) have sinusoidal time dependence, then \Phi(\textbf{x},t)=\Phi(\textbf{x})e^{i\omega t} Why would this equation be true? Why shoudnt the equations read \Phi(\textbf{x},t)=Im(\Phi(\textbf{x})e^{i\omega t})...
  42. S

    Finding the amplitude and phase of two sinusoidal motions

    Homework Statement Determine the amplitude and phase of the resultant motion when two sinusoidal motions having the same frequency and traveling in the same direction are combined, if their amplitudes are 3.0 cm and 4.0 cm and they differ in phase by pi/2 radians. Homework Equations...
  43. S

    Solving Sinusoidal Diff EQ: Lagrangian Equation Problem

    Homework Statement \ddot{\Theta}=C \sin{\Theta} where \Theta is a function of time, and C is a constant. I ran into this on a Lagrangian Equation problem, and though the problem doesn't ask for the solution, I'm wondering how one would solve this Diff EQ. I'm afraid my intro to Diff EQ...
  44. M

    Wave Motion of sinusoidal wave

    Homework Statement For a sinusoidal wave: At a certain instant, let point A be at the origin and point B be the first point along the x-axis where the wave is 60.0° out of phase with point A. What is the coordinate of point B? y = (15.0 cm) cos(0.157x - 50.3t) Homework EquationsThe Attempt...
  45. K

    Transverse sinusoidal wave on a string

    [SOLVED] transverse sinusoidal wave on a string Homework Statement The wavefunction of a transverse sinusoidal wave on a string has the form y(x,t) = A*cos(kx +omega*t + phi), where x and y are in m, t is in s and phi is the phase constant in radians. The wave has a period T = 24.2 ms and...
  46. C

    Completely Lost in this Physics Problem Sinusoidal transverse waves

    A sinusoidal wave is traveling on a string with speed 10.00 cm/s. The displacement of the particles of the string at x = 20 cm is found to vary with time according to the equation y = (5.0 cm) sin[16.0 - (8.0 s-1)t]. The linear density of the string is 7.0 g/cm. (a) What is the frequency of the...
  47. C

    Intersect of three sinusoidal functions

    hi, is it possible to find the intersect of three different sinusoidal functions without using a graphing calculator? here are the three equations: y=sin (2pi/23)(x) y=sin (pi/14)(x) y=sin (2pi/33)(x) The hint given is that the intersect occurs when y=1
  48. I

    Sinusoidal Voltage and frequency?

    Does the frequency of a sinusoidal voltage or current attribute anything? Maybe more power? All I know so far is that you can filter certain frequencies out with filter circuits.
  49. J

    What is the Coordinate of Point B in a Sinusoidal Wave?

    Homework Statement Consider the sinusoidal wave in the figure, with the wave function below. At a certain instant, let point A be at the origin and point B be the first point along the x-axis where the wave is 60.0° out of phase with point A. What is the coordinate of point B? y =...
  50. N

    Mechanical sinusoidal transverse wave

    [SOLVED] mechanical waves Homework Statement A sinusoidal transverse wave is traveling along a string in the negative direction of an x-axis. The figure shows a plot of the displacement as a function of position at time t=0; the y-intercept is 4.0m. The string tension is 6.8N, and its linear...
Back
Top