# Why can we hear the full range of square waves from 1 Hz-20 kHz, but not sine waves of the same frequencies?

I connected the output (50Ω) of a function generator to a 35 watt 5Ω speaker.

When I sent square wave signals of 1 Hz-20 kHz to the speaker, my friends and I were able to hear them. But when I sent sine waves across the same range, no one was able to hear anything below 100 Hz.

• you used a scope to confirm what the function generator is feeding the speaker yes? Aug 23, 2018 at 15:16
• Note that in addition to the frequency issues, this is a fairly weak and improper way to drive a speaker - a 5 ohm load on a 50 ohm source won't see much power transfer. If you actually wanted to explore the speaker capability and what you can hear, the first thing you would need is an amplifier suited to the speaker's load impedance. Aug 23, 2018 at 16:28

Most people can't hear sinewaves below about 20 Hz. The fact that you couldn't hear them until they got to 100 Hz is probably due to poor low-frequency response in your amplifier/speaker.

When you use a square waveform, you are adding a rich series of harmonics to the fundamental frequency — these are what you're hearing, and your brain extrapolates the fundamental frequency for you. Down to a point, that is — at some point you just start hearing individual clicks.

• Note that this ability to extrapolate is what allows small portable radios to seem to be able to play a wide range of musical frequencies, including bass notes which should not, by rights, be audible. The tiny speaker can't handle the excursions, and distorts the music to produce harmonics of the lower notes, which the brain then reconstitutes. Aug 24, 2018 at 4:10

The basic difference is that a sine wave is only a single frequency, but a square wave is actually made up of the fundamental frequency plus odd harmonics. So for example a 50Hz square wave isn't just 50Hz, but also 150Hz (3 x 50HZ), 250Hz (5 x 50Hz), 350Hz (7 x 50Hz) etc.

Amplitude decreases as the harmonic number increases, but may still be significant out to the 10th harmonic and beyond.

The other factor involved is the response of the human ear.

The ear is less sensitive to lower frequencies, and this gets worse as the sound level decreases. Below the threshold level you won't hear any sound.

With a square wave, the human ear's increased sensitivity at higher frequency more than makes up for the reduced amplitude of the harmonics. At ~25 dB SPL you may be able to hear the harmonics of a square wave whose fundamental frequency is below 100Hz, when a sine wave of the same frequency and amplitude is inaudible.

I connected output (50Ω) of function generator to 35 watt 5Ω speaker.

If you connected the generator directly to the speaker (without an amplifier in between) then the sound output will be very weak because:-

a) function generators are designed to produce a low power signal (typically 0dBm or 1mW) not drive a high power speaker.

b) there is a large mismatch between 50Ω and 5Ω, which greatly reduces the amount of power transferred.

c) the speaker also has a frequency response which drops off below its resonant frequency, and its impedance varies with frequency so when driven by a high impedance the frequency response is less flat.

All this means is that to get a good sound level you need to put an audio power amplifier between the generator and speaker.

All non-sine wave signals can be broken down into a collection of sine waves interfering with one another. This is done using a Fourier Transform. Each of the component sine waves are different frquencies, and when they come together in non-ideal scenarios, such as a real finction generator, they dont quite create a perfect imitation of the signal they are trying to create. So the square wave you're sending through the speaker is not a perfect square wave. Thus you are probably hearing mostly noise and some of the component fequencies as well.

• There are elements of truth in this, but the conclusions are fairly mixed up and mistaken. For purposes of the question it really matters little if the square wave is perfect or not, the components that would be audible are the medium frequency ones, which distinguish it from a sine wave. In contrast those that would make it very sharply square are potentially too high in frequency to be audible. Aug 23, 2018 at 16:24

Perhaps you've connected a bare loudspeaker with no baffle (box) around it to your signal source?
At low frequencies, air pushed or pulled out the speaker's front simply whips around to its back, and is poorly radiated to your ear. At a high-enough frequency, this process is foiled by speed-of-sound and you hear a louder sound. A speaker mounted in a baffle-board or stiff wall increases the front-to-back path length, which extends the low-frequency audible response.
And as others have mentioned, a pure single-frequency sine wave ensures that what you hear is a pure tone at the frequency displayed by your function generator. A square wave includes 3X, 5X, 7X, 9X frequencies in addition to the 1X frequency displayed by your function generator. The square wave harmonics (those other than 1X) are more clearly audible than the 1X frequency, for function generator frequencies below about 100 Hz.