Sound and sound waves / Guidelines Tricks and Tips
Sound and sound waves | Introduction
There is not doubt!
Probably the majority of us came across a sine wave when dealing with sound. But what is the connection between that trigonometric function and propagation of sound in practice. Is it so, that our ear is constantly hit with some weird wavy-shaped air turbulences? How come the sound wave can be 17 metres long, and yet we are still be able to hear it in areas with much smaller dimensions. Is there a connection between the acoustic pressure and the atmospheric pressure. After reviewing some basic terms related to sound, we will be able to easily answer those and a couple of other questions.
Speaking of sound?
When speaking of sound, some of us think of such terms as vibration, sound wave, sound pressure, others will think of speech, music, noise, or even sine waves, frequencies, amplitudes and wave lengths and phase.
Regardless of the first associations, those the basic problems related to receiving auditory sensation i.e. hearing sounds. I will briefly try to describe then, and the relations between them
The sound is produced by vibration
We deal with air as a carrier of these vibrations on a daily basis. (although they may be carried by liquids, like water, or solid materials, such as concrete)
When air molecules are out of balance, and start swinging, from side to side, moving neighbouring molecules, it creates deviation from the atmospheric pressure are being created i.e. the sound pressure.
The simplest and the best known example is periodic (repeated over time) sine wave – a simple tone.
The chart above shows the movement of a single particle. To simplify: as a result of vibration e.g. guitar strings, the molecule leaves it’s equilibrium position. ( the string leanes forward and starts pushing the air molecules.
The particles start pushing their „neighbours” and keep moving until they reach the maximum deflection. Then they go back, due to changes in pressure and elastic forces, reaching maximum deflection on the opposite side of the point of balance. And so on. As the sound is decaying, the movements become smaller and smaller, until they eventually stop.
Absolute silence means that none of the molecules are moving.
Although, we do not face such phenomenon on everyday basis, just because we are always surrounded by background sound i.e. movement of air molecules.
How does it works?
Those group of moving particles cause small (compared to atmospheric pressure) changes in pressure. The human ear receives those changes in pressure and transmits them to the brain as a listening experience.
To understand what kind of sound pressure levels we are dealing with, and to make a comparison (to atmospheric pressure), I will tell you that loud music has a sound pressure level of 94 dB, which corresponds to a pressure of 1 Pa, or about 10000 times less than atmospheric pressure (1000 hPa = 10 000 Pa).
I would compare a sine wave to an atom, it is the basic ingredient of all sounds. (even noises are made up of sine waves of continuously varying amplitudes and phases), so it is quite useful and important when we are thinking of sounds.
Vibrations must occur 20 times per second, so we could be able to hear anything, this comes from the construction of the human ear.
So, we got to the oscillation frequencies.
Frequency is characteristic of sine waves, it tells us how many complete cycles occur within 1 second time. The unit of frequency is Hertz [Hz] and is marked by the letter f. In the example above, the wave has a frequency of 1 Hz, which means that every second, a molecule gets from the position of equilibrium to the top (maximum deflection), then bottom (maximum deflection), then it goes back again to the equilibrium position.
For comparison, below it’s a wave with a frequency of 20 Hz
We are not able to hear a simple tone with a frequency of 1 Hz, due to the structure of our ear, we can receive sounds from the range 20 Hz – 20 000 Hz. Any sound with a frequency below 20 Hz is an infra sound, they can be heard by some animals, e.g. elephants. Every sound above 20 kHz is an ultrasound, those can be heard by „chosen ones” as well, animals like dogs.
Physics and psychoacoustic
Physics is good, but we are more interested in more practical approach to the subject. Sound F
The frequency of sound (physical unit) is directly related to the pitch of sound (a sensual quality). The higher the frequency, the higher the sound, the lower the frequency, the lower the sound.
Additionally, there is a simple relation between frequency and pitch. Each doubling is an interval of an octave.
For example, C1 has a frequency of 32.7 Hz, therefore the sound from a higher octave will have the frequency of 2 x 32.7 = 65. 4. The same will go for C2: 65,4 x 2 = 130,8 Hz etc.
WARNING!
Of course it’s quite simplified. Mel scale exists, a perceptual scale of pitches, judged by listeners (so it’s quite subjective) to be equal in distance from one another. 1000 mels are defined as 1000 kHz with the SPL level of 60 dB SPL.
To a certain level (approximately 1 kHz), it coincides with what I wrote (frequency doubling = an octave). Above 1 kHz there are considerable differences (which are getting bigger and bigger for higher frequencies).
If someone is interested in this subject, he can search information about mel scale (e.g. F. Alton Everest, Podręcznik Akustyki, PLN), but I think that the adoption of the frequency doubling as an octave is sufficient, so I won’t be talking about mel scale again.
The inverse of the frequency of vibration is the period, marked by the letter T. The period is the time, it takes for a vibrating object to complete it’s cycle. It is measured in seconds. Between the frequency and the period we observe the following relations:
where:
f – frequency [Hz]
T – period [s]
Knowing the frequency, we can easily calculate the period and vice versa. For example, a wave with a frequency of 20 Hz has a period of 1/20 sec, or 50 ms. Whilst the wave with a period of 2 ms has a frequency of 1/0,002 = 500 Hz.
Another important characteristic for harmonic vibrations (and therefore sine waves) is wavelength. Wavelength is the distance between crests.
The wavelength depends on the speed of the wave, therefore the wavelength of 1 kHz propagated in the air will differ from the wavelength doing the exact same thing in the water.
The wavelength is the product of the velocity of the wave and its period, it is denoted by the symbol lambda λ. We can therefore be calculated knowing the velocity of the wave and its duration or frequency:
or:
where:
λ – wavelength [m]
v – velocity of the wave [m/s]
T – period [s]
f – frequency [Hz]
The speed of sound in the air is about 340 m/s, knowing this value, we can easily calculate the limits, whithin which acoustic waves are located.
for 20 Hz:
λ = 340/20 = 17 m
for 20 kHz:
λ = 340/20000 = 0,017 m = 1,7 cm
Therefore acoustic wavelength (spreading in the air) are in the range of 1,7 cm – 17 m. So if the wave is 17 metres long, it doesn’t mean that we won’t be able to hear it in a room of a smaller dimensions: typical small room: 2,5m x 3,5m x 4,5m.
Waveform (in this case, the famous sine) is a record of pressure changes in a single point. It’s like if we put a thermometer on the table and kept heating it up and cooling it down, at the same time taking notes about the temperature changes. The same way we register the changes of pressure, using an appropriate meter. Instantaneous changes in the air affect the eardrum and cause it to vibrate.
Thus the room’s dimensions are not needed to be bigger than the waves dimensions. We will hear it anyway. The room dimensions will only cause the wave to have negative phase relations, but it will certainly be heard.
As you can see from the formula, the wavelength is inversely proportional to frequency, the higher the frequency, the smaller length and vice versa.
Another parameter, which I will present is amplitude:
The amplitude of a sine wave is the maximum vertical distance reached in either direction from the centre line of the wave.
It’s quite obvious, so no further explanations needed.
And finally a parameter, that will link us with the second, the practical part of the subject – phase. Phase is the time difference between two sources (signals). The signals may overlap (then they are in phase), they also can be offset. Here are some examples
In the case of identical sine waves offset by 180° (commonly known as anti-phase), it’s just silence. It happens because, as you can see in the chart the second one is the opposite of the first one.( When dealing with Waves addition the same rules apply, and it is similar to vectors addition).
When the signals are offset by 360° , the situation is almost identical to the situation with no offset. The only difference is that the signal begins a moment later. (1 period). We’ve got to deal with phase problems, not only when we are recording something, but when where playing sounds as well. There are special microphone’s techniques that minimise the impact of phase offsets. (for sound recording, when using more than 1 microphone)
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