MathGroup Archive 1999

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Re: Sound and Mathematica

  • To: mathgroup at
  • Subject: [mg19779] Re: Sound and Mathematica
  • From: "Stephen P Luttrell" <luttrell at>
  • Date: Fri, 17 Sep 1999 01:36:38 -0400
  • Organization: Defence Evaluation and Research Agency
  • References: <7rnjrt$>
  • Sender: owner-wri-mathgroup at

> I've a problem with mathematica: I want to create a sound which
> includes all frequencies between 20 Hz and 20 000 Hz. The sound should
> begin at 20 Hz and stop at 20 000 Hz and should increase linearly. For
> testing it, I used the following mathematica command (20 - 4000 Hz):
> (Later I want to replace 4000 by 20 000)
> Play[Sin[4000 t 2 Pi t], {t, 0, 1}]]
> But the frequency, on which this generated sound stops was much more
> higher than 4000 Hz! What's my mistake?

Frequency is the instantaneous rate of change of phase, divided by 2 Pi.
Differentiating your 4000 t 2 Pi t with respect to t (and dividing by 2 Pi)
gives 2 4000 t, which is equal to 8000 when t=1. To correct for this, you
need to include an additional factor of 1/2 in your original expression for
the phase.

Dr Stephen P Luttrell
Room EX21, Defence Evaluation and Research Agency
Malvern, Worcs, WR14 3PS, U.K.
luttrell at
01684-894046 (phone), 01684-894384 (fax)

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