0
$\begingroup$

Can anyone explain the equation $\sin(fπx)$ where $f$ is a sound wave's frequency in Hz?

I am trying to convert sound waves into graphed sine waves by using their frequency but don't understand the formula. Why are we multiplying by $\pi$?

If anyone knows another equation to graph the sound like a sine wave I would be very grateful... I found this equation online and it doesn't seem right...

Improve this question
$\endgroup$
2
  • $\begingroup$ Frequency is one over the period. So by definition, the sound wave repeats itself every $f^{-1}$ units of time. The wave at time zero must be equal to the wave at time $f^{-1}$. This is true for the expression you give. It would not be without the pi. $\endgroup$
    – Connor Behan
    Commented Aug 31, 2021 at 14:18
  • 1
    $\begingroup$ If you want your equation to describe a moving wave, the (f) and (x) should be separated : a = A sin[2π(f t - x/λ)]. $\endgroup$
    – R.W. Bird
    Commented Aug 31, 2021 at 18:16

1 Answer 1

Reset to default
2
$\begingroup$

The amplitude of a sine wave with frequency $f$ Hertz at time $t$ seconds is

$$a(t) = A_0\sin(2\pi ft)$$

where $A_0$ is the maximum amplitude. The argument to the $\sin$ function is in radians, which is why we need to multiply by $2\pi$, which is one revolution in radians. This means that the amplitude $a(t)$ repeats every $\frac 1 f$ seconds.

Improve this answer
$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.