# How are sounds recorded and reproduced (played back)?

Someday I have suddenly got wondered how sounds are recorded and reproduced. I searched a little bit but the information I got was composed of difficult words and contents, so I couldn't understand that.

According to what I've read, the reason sounds can be reproduced is because of a vibration of diaphragm(?). But I think that doesn't make sense, because how one thing can reproduce various sounds having different waveforms? To me, it sounds like that violins can produce sounds of flutes.

(Of course in this video a piano imitates a human voice, but what I'm talking about is a waveform, not a synthesis of waves. (I have totally no idea how a piano can make a human voice, but my guess is as follows: splitting a recorded sound over time → mimicking that short wave by using piano sounds))

After thinking for a while, I realized that my question was divided into 3 parts and I would like to know how all of the questions are achieved in analog and digital manners.

(1) Capturing 'what' of sounds? (recording) // Maybe sound pressure? volume(amplitude)? but how?

(2) How are the recorded data stored?

(3) How can the recorded data be reproduced into the real sound?

I read that digital sound recording is achieved by sampling, quantization, and encoding but I think only the first one is related to this question. As I commented on (1), sampling what and how?

Currently I'm absolutely seriously curious about it. I really would like to know. It would be appreciated if you share some of your knowledge to me. Thank you for reading this long question. (Please let me know if this place is not a right place to ask this kind of question.)

A big question. Plz have a look at this first https://en.wikipedia.org/wiki/Sound_recording_and_reproduction.

Sound is highly related to vibration. Sound is generated by vibration of a sound source, and you can hear a sound is because of the vibration of eardrum.

## Sound Recording

Sound pressure is the local pressure deviation from the ambient (average or equilibrium) atmospheric pressure, caused by sound wave, and often denoted by $$p$$, or more precisely, $$p(x, y, z, t)$$, which means that it is a function of position $$(x, y, z)$$ and time $$t$$. Sound pressure is a scalar quantity that has no direction. If we fix the location $$(x, y, z)$$ as constant, the sound pressure only depends on time variable $$t$$, which makes it a simple $$p(t)$$. Therefore, we can plot the sound pressure vary against time:

The x axis is time and the y axis is sound pressure. A pretty simple curve.

Now we want to record this curve using a microphone. The microphone has a membrane which is affected by the force generated by the sound pressure ($$F=pS$$), resulting in a displacement. Then convert this vibration signal to electric signal (electromagnetic induction) and finally digitize this electric signal and store it.

## Sound Reproduction

Since we successfully recorded a sound signal, now send this digital signal into a digital-analog converter to get an analog electric signal. Use this electric signal to excite a loudspeaker and make the diaphragm vibrate and radiate sound wave to the air. As you may already notice that microphone and loudspeaker realize the opposite energy conversion process - acoustic to electronic and electronic to acoustic, they are called electroacoustic transducer.

• Thank you! your answer helped me a lot. I would like to know what does 'S' mean in the above formula 'F=ps'. And If you don't mind me asking, I would like to ask you one more question. This document(developer.mozilla.org/en-US/docs/Web/Media/Formats/…) says, "To provide additional room ... an additional 2.05 kHz transition band is added". But since I'm not good at math, I couldn't understand what 'room' means in that context and what is transition band. Could you please explain what they mean? Thank you.
– Cor
Jan 20 at 17:02
• @Cor Pressure is defined as force per unit area, $P=F/S$, so is sound pressure. $S$ in the formular means the area of the membrane. Jan 20 at 23:09
• @Cor And for that document's saying, we know that human hearing range is 20 Hz to 20 kHz, and according to Nyquist sampling theorem the sample rate should be at least twice of the highest frequency (or bandwidth for bandlimited signal), that's 40 kHz. However we should apply a lowpass filter to filter out all the frequency components above 20 kHz to avoid aliasing, and an ideal lowpass filter do not exist, so in practice, sampling rate is often a little higher than twice of the highest frequency, which is the meaning of the additional room. Hence we use 44.1 kHz as sample rate. Jan 20 at 23:22

Sound is a compression wave in a fluid media. In other words: sound is air molecules wiggling back and forth. No air = no sound.

Sound is generated if something vibrates and jostles the air molecules. For example: if you hit a drum head, the head gets displaced and wiggles back and forth for a bit. This in turn wiggles the air around it. The moving air molecules bump into other air molecules and so the wiggling propagates through the entire air in the room.

That means that the air wiggles your ear drums and moves the air drum a bit. This motion gets transferred to nerve endings in your inner ear that are sensitive to being wiggled. When they do, you hear something!

Capturing 'what' of sounds? (recording) // Maybe sound pressure? volume(amplitude)? but how?

You capture sound with a microphone. You can put it anywhere where there is wiggling air. The air jostles the "membrane" of the microphone and this motion is converted to a proportional electrical signal (as a function of time). Microphone signals are either proportional to the sound pressure or the velocity (or a combination of both) of the air molecules.

How are the recorded data stored?

Once you have an electrical signal, it can be stored in various different ways. By far the most popular one these days is digital. The signal is converted by an Analog to Digital Converted to a list of numbers and then stored in computer memory or drive.

How can the recorded data be reproduced into the real sound?

Using a Digital to Analog Converter you turn the numbers back into an electrical signal. This in turn gets converted into sound by a loudspeaker. The most common one is the "electrodynamic" loudspeaker. The electric signal (after proper amplification) drives a magnet and that magnet moves a membrane or "cone" back and forth. The cone jostles the surrounding air molecules and we are back where we started: If there are wiggling air molecules there is sound!

• Thank you very much! Your answer helped me a lot. It was my mistake that I had had thought a thing like a string's vibration was only a vibration. I couldn't think a membrane's electrical movement to cause sound pressure was also a vibration. Thank you again!
– Cor
Jan 20 at 17:25