# time in Sine Wave equation

According to Wikipedia,

The sine wave or sinusoid is a mathematical function that describes a smooth repetitive oscillation.

The formula for the Sine wave is,

A = Amplitude of the Wave ω = the angular frequency, specifies how many oscillations occur in a unit time interval, in radians per second φ, the phase, t = ?

Here ω, is the angular frequency i.e ,

It defines how many cycles of the oscillations are there.

Now let see the frequency,

Frequency is the number of occurrences of a repeating event per unit time

For example, if 100 events occur within 15 seconds the frequency is:

Events = 100;
Time = 15;
FREQ = Events/Time;


Which means there is total 100 cycles of wave in 15 seconds , am i correct ?

Events = 71;
Time = 15;
FREQ = Events/Time;
W = 2*PI*FREQ;   % 2*PI for circular path
A = 2 ;


Now what is the use of small 't' ? in the Sine wave equation , what time is it ?

In the context that you described, $t$ is a variable indicating time. That is, the wave will take on a value of $y(t)$ at the time instant $t$. If this is measured in seconds, then $\omega$ specifies the number of radians that the wave passes through in one second. And, as you noted, if the wave has a frequency of $\frac{100}{15}\ \text{Hz}$, then it will pass through 100 periods in 15 seconds.

Well to clear your doubt ,i would like you to ask you a question. What would be the value of angular frequency × Time period = ??

Okay,so in eq - $$\omega \times t$$ . if we put $$T$$ in place place of $$t$$, given that the wave is sinusoidal, the value to that eq would be $$2\pi$$. By definition $$T$$ is the time taken to complete one oscillation so when we put $$T$$ in place of $$t$$ , the value we get from the equation is - $$2\pi$$(as total distance traveled by a waves particle of a sinusoidal wave in time $$t$$=$$T$$ = $$2\pi$$). So we can say that significance of $$t$$ in the eq is that it tells the position of the wave's particle at time $$t$$ (note that I stated position of waves particle and not the wave itself because it that case we have another eq that is $$\lambda = vT$$ )

This equation works just like Distance =speed × time .

• Hello Animesh and welcome to SE. Posting questions as answers is not exactly the best way to help people. You could very well post that as a comment if you feel it can help though. Commented Mar 1, 2020 at 11:45
• Haha. I just want people to think on their own. The way he has described the question ,it seems that he doesn't care about the concept and just want to get to the answer real quick. Commented Mar 1, 2020 at 18:37
• Understood, but still you could had done the same in a comment Commented Mar 1, 2020 at 20:18

whenever you see the equation

Y= A Sin(wt+ @), the (wt+ @) section indicates a degree or radian value.With that in mind take Wt.

-From what we know W is angular frequency.That means Period or Cycle per second. in our case if we opt to take it in Radians ,then its 2π/time. If we take it in degrees then it becomes 360degrees/time. Its also revolutions per second.

-Again from what we know @ is an angle either in radians or Degrees

therefore if we take wt which is 2π/time,360degrees/second e.t.c and multiply it by (t).We are left with an angular value.. therefore wt is an angle that can be added to @ to get a phase value

think of it as Y= A Sin ( [22π/time] x t + 4π ) equals to Y= A Sin ( 22π + 4π )

or in degrees .

Y= A Sin ( [140degrees/time] x t + 40degrees ) ,Y= A Sin ( 140degrees + 40degrees )

• Please us LaTeX to write math text. Commented May 13, 2020 at 10:11