Playing the frequencies of the Audiogram

Andy Long
Summer, 2022
Retraining Your Brain: Rebraining

On a suitable computer system, this plays a pure tone with a frequency of 440 hertz for one second:

Play[Sin[2π 440 t],{t,0,1}]

A pure tone at 3000 Hertz:

play=Play[Sin[ 2π 3000 t],{t,0,2}]

(RefLink[Play, paclet:ref/Play]) is set up so that the time variable that appears in it is always measured in absolute seconds. When a sound is actually played, its amplitude is sampled a certain number of times every second. You can specify the sample rate by setting the option (RefLink[SampleRate, paclet:ref/SampleRate]).

Specifying the sample rate for a sound.

In general, the higher the sample rate, the better high-frequency components in the sound will be rendered. A sample rate of r typically allows frequencies up to r/2 hertz. The human auditory system can typically perceive sounds in the frequency range 20 to 22000 hertz (depending somewhat on age and sex). The fundamental frequencies for the 88 notes on a piano range from 27.5 to 4186 hertz.

Audio[File["ExampleData/car.mp3"]]

The highest frequency in hertz that can be present in a particular sound is equal to half the setting for (RefLink[SampleRate, paclet:ref/SampleRate]).

play=Play[Sin[ 2π 110 2^Floor[t]* t],{t,0,8},SampleRate->128000]

play=Play[Sqrt[t] Sin[ 2π 110 2^Floor[t]* t],{t,0,8},SampleRate->128000,PlayRange->{0,1}]

play=Play[t^2 Sin[ 2π 110 2^Floor[t]* t],{t,0,8},SampleRate->128000,PlayRange->{0,1}]