A Brief Intro to Sound, Wave, and Electronics

Sound plays a crucial role in everyday life across various aspects. From communication to entertainment, sound is an integral part of our daily experiences. In this article, we are going to figure out how sound is transmitted and how to use electronic devices to produce sound.

To engage with sound using electronic methods, we just need

• a speaker
• a function generator

Speaker is common and cheap; it could be found in most electronics store. However, selecting a function generator could be complex, I will give more explanation in the following sections.

Sound is a form of energy that travels through a transmission medium, such as a gas, liquid or solid, as waves. These waves are created by vibrations, which occur when an object or substance moves back and forth rapidly. When these vibrations reach our ears, they are converted into electrical signals that our brain interprets as sound.

      Tuning fork is an excellent demonstration of how sound is generated. A tuning fork is a metal instrument with two prongs that can vibrate when struck against a surface. When the tuning fork vibrates, it creates sound waves in the surrounding air.

A tuning fork by John Walker stamped with note (E) and frequency in hertz (659), from Wikipedia

Motion of an A-440 tuning fork (greatly exaggerated) vibrating in its principal mode, from Wikipedia

By observing a tuning fork in action, you can visually see and audibly hear how vibrations lead to the generation of sound waves, providing a tangible demonstration of the physics of sound.

In physical perspective, a wave refers to a disturbance or variation that propagates through a medium or space, carrying energy without necessarily transporting matter along with it. In mathematical perspective, waves can be described and understood using mathematical equations.

Sine wave is one of the most simple and common waves.

A sine wave is a mathematical curve that describes a smooth, periodic oscillation.

Mathematical, it is defined by the function

y= A⋅sin(Bx+C)+D

where A is the amplitude, B is the frequency, C is the phase shift, D is the vertical shift, x is the independent variable (usually time), and sin represents the sine function.

Amplitude:

The amplitude of a sine wave represents the maximum displacement from the equilibrium position. It determines the height of the wave's peaks and the depth of its troughs.

Frequency:

The frequency of a sine wave refers to the number of cycles (oscillations) completed per unit of time, usually measured in hertz (Hz), which is equal to one cycle per second. Higher frequencies correspond to shorter periods and more rapid oscillations.

It is important to remember that the sound wave that can be heard by human is between 20 to 20000 Hz. Different animals can hear sounds at different frequencies, both dogs and cats can hear the sound that above 20000 Hz. Therefore, pets sometimes might be unrest because they hear the sound human cannot hear.

Phase Shift:

The phase shift in a sine wave determines the horizontal displacement of the wave along the x-axis. Positive phase shifts move the wave to the right, while negative phase shifts move it to the left.

Vertical shift:

The vertical shift is like phase shift but along the y-axis, positive phase shifts move the wave to the top, while negative phase shifts move it to the bottom.

Here are sine waves with different parameters (I use desmos to make the graphs).

Y = sin(x), Y = 2sin(x), Y = 4sin(x)

Y = sin(x), y = sin(2x), y = sin(4x), y = 2sin(4x)

Y= sin(x), y = sin(x + pi/2), y = sin(2x + pi/2), y = 2sin(x + pi/2)

Y = sin(x), y = sin(x) + 1, y = sin(2x) + 1, y =2sin(x)+1

I have introduced the nature of sound and wave, then how to present them electrically?

The speaker can convert electrical energy into kinetic energy and generate waves through vibration. If we control the voltage conversion period between 20 and 20,000 Hz, the speaker should produce sound waves that can be heard by humans.

This bring out a question: how can we generate a stable wave with its frequency is above 20 Hz but under 20000 Hz? Fortunately, we have function generators. A function generator is an electronic device generates electrical signals with adjustable frequency, amplitude, and waveform to meet various experimental or testing needs.  

Since function generators are used in different fields, they come with different features. Basic function generators may only generate simple waves with a narrow frequency range, while the advanced one could produce complex hybrid waves and offer more choices on parameters.

If you have searched online shops, you may have noticed that the frequency range is the main driver of price. The good thing is, for this sound experiment, we don't need a wide frequency range, which means we could find a device that meets our needs at a relatively low price. If you want to learn more about electronics in the future, I strongly suggest finding a professional device, as an advanced function generator typically includes the 'backward compatible' function.

In the following steps, I will only use a small portable function generator for a clear demonstration.

Connecting the speaker and function generator first, and then turn on the function generator, select an amplitude(voltage) and frequency, we can hear sound coming from the speaker.

Make a few more attempts, feel the sounds. You may feel that at one frequency, the sound sounds more comfortable and distinguishable, while at another frequency, the sound sounds a strong feeling of dropping.

Here, I need to introduce another concept: pitch.

Sounds that have obvious rules for vibrating and can be clearly distinguished and imitated are pitches. For example, the sound of musical instruments and the music on the radio are both can be identified as a series of pitches.

Pitches of different frequencies have different names. In music, the letters A to G are usually used to represent the notes, and then they are repeated starting from A. A C note that is one octave above C is usually labeled as a high C, while a C note that is one octave below is usually labeled as a bass C. C major is a series of the simplest pitches because it does not contain any sharps or flats and all notes are natural.

The frequencies in C major that based on the standard pitch A = 440Hz are listed below:

C - do - 261.6HZ

D - re - 293.6HZ

E - mi - 329.6HZ

F - fa - 349.2HZ

G - sol- 392HZ

A - la - 440HZ

B - si - 493.8HZ

The frequency of the standard tone A1 is 440HZ, and the frequency of A2, which is an octave above A1, should be 440HZ×2=880HZ. For another example, the frequency of the standard tone a1 is 440HZ, and the frequency of the octave A below it should be 440HZ÷2=220HZ.

In this video, I set the frequency from C6 to B7, which makes it easier for my phone and the speaker to capture the sounds.

Next, I will write an article about timbre and volume, so that we can replace this monotonous and harsh electronic sound.