Amplitude modulated signals sound rough to the human ear. The perceived roughness increases with modulation frequency, then decreases, and eventually disappears. The point where roughness reaches is maximum depends on the the carrier signal, but for a 1 kHz tone roughness reaches a maximum for modulation at 70 Hz. Roughness also increases as a function of modulation depth.

Amplitude modulation multiplies a carrier signal by

1 + *d* sin(2π *f t*)

where *d* is the modulation depth, *f* is the modulation frequency, and *t* is time.

Here are some examples you can listen to. We use a pure 1000 Hz tone and Gaussian white noise as carriers, and vary modulation depth and frequency continuously over 10 seconds. he modulation depth example varies depth from 0 to 1. Modulation frequency varies from 0 to 120 Hz.

First, here’s a pure tone with increasing modulation depth.

Next we vary the modulation frequency.

Now we switch over to Gaussian white noise, first varying depth.

And finally white noise with varying modulation frequency. This one sounds like a prop-driven airplane taking off.

**Related**: Psychoacoustics consulting