# What does an amplitude modulated signal sound like in a speaker?

Let us compare two signals: One is a normal sinusoidal signal with single frequency of 5kHz with 1V amplitude (2V peak-to-peak) while th other signal has a carrier frequency of 5kHz and 2V peak-to-peak, but is an AM modulation signal with modulation waveform frequency (or message frequency) of 900Hz, with some modulation index.

Connect these two signals generated by function generators to aspeaker, generating sounds.

Would both signals sound similar in pitch (frequency) to our ears, or would the modulated signal's pitch sound more like 900Hz than 5kHz?

• Just try it and see. Oct 15 '14 at 7:11

Sounds are hard to describe in words, so the best thing to do is simply try it. You will hear the 5 kHz, but it will sortof "buzz" at 900 Hz.

Even if you don't have equipment that does AM modulation, just create a WAV file with this signal and play it thru the PC speakers. Hearing it yourself is really the only way to answer this question.

• You sure about the 900Hz hum? A fourier transform of an AM signal is basically a convolution of the carrier with the signal, isn't it. In that case, with a 5kHz carrier modulated with a 900Hz sine, you'd hear a mix of three tones: 4100Hz, 5000Hz and 5900Hz (the carrier and 5kHz +/- 900Hz).
– RJR
Oct 14 '14 at 23:57
• @Olin: How would you do that, exactly? Oct 15 '14 at 0:09
• Keep in mind a speaker isn't perfectly linear, so there will be some intermod producing 900 Hz energy. Human hearing isn't linear either. Oct 15 '14 at 0:42
• @RJR: That's what the math says, but not what your ears will hear. Again, sounds are really hard to describe in words, so just try it. Oct 15 '14 at 12:09
• @Olin: Why, create a .wav file which would allow me to recreate what you heard, of course. Oct 15 '14 at 12:18

I am aware this question is old, but as I needed the solution and couldn't find a better one, I'm writing here the best answer I could manage.

Short answer: the modulated wave sounds like two notes near the higher note played simultaneously.

Long answer: For simplicity sake we will assume a modulation index of 1.

The function of an amplitude modulated sound is $$\ f(t)=A\cdot sin(t \cdot F_1)\cdot sin(t*F_2) \$$

where A is the amplitude $$\F_1\$$ is the first frequency and $$\F_2\$$ is the second frequency. (it doesn't matter which one is the carrier and which one is the regular frequency)

It doesn't matter if you take the long route of doing a Fourier transform, the short route of remembering trigonometric identities or the shortest route of checking Mathematica. the point is that the this function is equivalent to $$\f(t)= \frac{A}{2} cos(t\cdot x(F_1-F_2) )+\frac {A}{2} cos(t\cdot x(F_1+F_2) ) \$$

(reminder: a sine and a cosine are equivalent except for a change in phase)

so we got the function of the notes that are equivalent to our original sound:

• A note with frequency equivalent to the difference in frequencies, and half the amplitude. (in your case a 4.1 kHz note)

• A note with frequency the sum of our original notes, and half the amplitude. (in your case a 5.9 kHz note)

I just tried this out with my HP3312 function generator directly driving a 5 inch speaker. The difference between unmodulated and modulated at the frequencies suggested (5 kHz carrier and 900 Hz modulation) is discernible but hard to describe. To me it sounded like the modulated signal was still a single frequency but a higher pitch. However, as the modulation frequency was lowered and as Olin suggested, it definitely changed into a buzzing sound especially for modulation frequencies below about 200 Hz. I was using near 100% modulation to try to maximize the effect. You should definitely try this out yourself, however, since everybody's ears are different.

To be "complete", if the degree of "distortion" is of order 3,

$$\Vs= a0 +a1*vg +a2*vg^2+a3*vg^3\$$

Where $$\vg:= sin (y)*sin (z): y= 5000 ; z = 900 :\$$

you will be able to hear this ...

$$\{1.250000} + 0.125000 * cos (8200) - 0.250000 * cos (1800) - 0.250000 * cos (10000) + 0.125000 * cos (11800) + 0.781250 * cos (4100) - 0.781250 * cos (5900) + 0.031250 * cos (12300) - 0.093750 * cos (2300) - 0.093750 * cos (14100) + 0.093750 * cos (7700) + 0.093750 * cos (15900) {- 0.031250 * cos (17700)}\$$ ...

if your ear can hear from 100 Hz up to 16 kHz (except 17700 ?).