Intersections betweens sinusoids

  • Thread starter mnb96
  • Start date
  • Tags
    Sinusoids
In summary, The speaker is facing a problem of finding the intersection points between two sinusoids with varying amplitude, frequency, and phase difference. They have not been able to find a solution through general methods or online resources, and suggest approximating the sines using Taylor series or perturbation series in order to find a solution. The course of action depends on the desired outcome.
  • #1
mnb96
715
5
I'm facing the following problem which sounded simple but apparently it is not (at least for me):

I have two sinusoids: different amplitude, different frequency, different phase difference and I want to find the intersection points, which is equivalent to solving the following equation in [tex]\theta[/tex]:

[tex]A_{1}sin(f_{1}\theta+\phi_{1}) = A_{2}sin(f_{2}\theta+\phi_{2})[/tex]

I was not able either to solve the problem in the general case, nor to find a solution around the net.
 
Physics news on Phys.org
  • #2
I don't believe that a solution formula exists at all, although I cannot prove this claim. I'm afraid you'll have to approximate. For example write the sines as second order Taylor series close to some zero, and solve an approximation there. Or then some kind of perturbation series.

What one should do of course depends on what one wants.
 
Last edited:

1. What are sinusoids?

Sinusoids are mathematical curves that are characterized by their repetitive and oscillatory nature. They are commonly represented by the sine and cosine functions, and can be found in various natural phenomena such as sound waves, electromagnetic waves, and alternating currents.

2. How do sinusoids intersect?

Sinusoids can intersect in two ways: they can either cross each other, or they can overlap. When two sinusoids cross, they have the same amplitude and frequency but are out of phase with each other. When they overlap, they have different amplitudes and frequencies but share the same phase.

3. What is the significance of intersections between sinusoids?

Intersections between sinusoids are important because they help us understand the behavior and properties of these curves. They can also be used to analyze and predict the behavior of systems that exhibit sinusoidal behavior, such as electrical circuits, musical instruments, and communication devices.

4. How can we mathematically represent intersections between sinusoids?

The intersection of two sinusoids can be represented using trigonometric identities and equations. These can help us find the exact points of intersection, as well as determine the resulting amplitude, frequency, and phase of the intersecting sinusoids.

5. Can sinusoids intersect at multiple points?

Yes, sinusoids can intersect at multiple points. The number of intersection points depends on the frequencies of the sinusoids and their relative phases. When two sinusoids have the same frequency and phase, they will have an infinite number of intersections. However, if their frequencies are different or they have different phases, they will intersect at a finite number of points.

Similar threads

B Having trouble deriving the volume of an elliptical ring toroid
    • Calculus
Replies
4
Views
338
B Intersection of line and curve
    • Calculus
Replies
14
Views
1K
I What is the approximation used here?
    • Calculus
Replies
3
Views
782
I Solutions to Simple Harmonic Motion second order differential equation
    • Mechanics
Replies
1
Views
409
I Question about Penning Trap
    • Classical Physics
Replies
1
Views
457
Aliasing, Continuous sinusoids and discrete sinusoids....
    • Computing and Technology
Replies
3
Views
811
Solving Curl A in Spherical Coordinates: Tips & Hints
    • Advanced Physics Homework Help
Replies
1
Views
798
Sinusoidal Radiation Statements (T/F)
    • Introductory Physics Homework Help
Replies
2
Views
349
I Taylor series and variable substitutions
    • Calculus
Replies
3
Views
1K
I How to evaluate the enclosed area of this implicit curve?
    • Calculus
Replies
2
Views
2K

Hot Threads

Recent Insights

Back
Top