# Generating a sound with pitch like Sin[2Pi t] as t steps from 0 to 1

I am trying to generate a sound with pitch that goes up and down like a sine wave from 0 to 2Pi. So the pitch should be Sin[2Pi t] as t steps from 0 to 1. I thought the way to do this would be somehow in pseudocode like make

f = Integrate[E^(Sin[x] + 2), x];


And then

Play[Sin[f[t]], {t,0,2Pi}]


But it seems Mathematica can't integrate E^(Sin[x] + 2)?

So then I just fooled around and did

Integrate[(Sin[t] + 2), t]

2 t - Cos[t]

Play[Sin[(1.2^(2 t - 1 Cos[t])*1000)], {t, 0, 2 Pi}]


and it doesn't do what I want either...

There are two basic approaches. In one, you define the data that will be played as a list, in the other, you define a function and Mathematica fills out the list. To define things directly:

t = Range/11025;
f0 = 200;
wav = Sin[2 Pi (f0 + 10 Sin[2 Pi t]) t];
ListPlay[wav, SampleRate -> 11025] Variable t defines the time, 11025 is the (arbitrarily chosen) sampling rate, f0 is the center frequency, and the inner Sin gives the frequency modulation.

To let Mathematica make the decisions, you can use Play instead of ListPlay:

Play[Sin[2 Pi (200 + Sin[2 Pi 5 t]) t], {t, 0, 4}]