A sound wave is a wave process that occurs in gaseous, liquid, and solid media, which when it reaches a person’s hearing organs is perceived by him as sound. The frequency of these waves ranges from 20 to 20,000 oscillations per second. We give formulas for a sound wave and consider its properties in more detail.
Why does a sound wave appear?
Many people wonder what a sound wave is. The nature of sound is the occurrence of disturbances in an elastic medium. For example, when a pressure perturbation occurs in a certain volume of air in the form of compression, then this region tends to spread in space. This process leads to air compression in areas adjacent to the source, which also tend to expand. This process covers more and more of the space until it reaches a receiver, for example, the ear of a person.
General characteristics of sound waves
Consider the questions of what a sound wave is and how it is perceived by the human ear. The sound wave is longitudinal, it when it enters the ear conch causes vibrations of the eardrum with a certain frequency and amplitude. You can also represent these fluctuations as periodic changes in pressure in the microvolume of air adjacent to the membrane. First, it increases relative to normal atmospheric pressure, and then decreases, obeying the mathematical laws of harmonic motion. The amplitude of the changes in air compression, that is, the difference between the maximum or minimum pressure created by a sound wave, with atmospheric pressure is proportional to the amplitude of the sound wave itself.
Many physical experiments have shown that the maximum pressure that the human ear can absorb without harming it is 2800 μN / cm 2 . For comparison, we say that atmospheric pressure near the surface of the earth is 10 million μN / cm 2 . Given the proportionality of the pressure and the amplitude of the oscillations, we can say that the latter value is insignificant even for the strongest waves. If we talk about the length of the sound wave, then for a frequency of 1000 vibrations per second, it will be a thousandth of a centimeter.
The weakest sounds produce pressure fluctuations of the order of 0.001 μN / cm 2 , the corresponding amplitude of the wave oscillations for a frequency of 1000 Hz is 10 -9 cm, while the average diameter of air molecules is 10 -8 cm, that is, the human ear is an extremely sensitive organ.
The concept of sound wave intensity
From a geometric point of view, a sound wave is an oscillation of a certain shape, but from a physical point of view, the main property of sound waves is their ability to transfer energy. The most important example of energy transfer by a wave is the sun, whose radiated electromagnetic waves provide energy to our entire planet.
The intensity of a sound wave in physics is defined as the amount of energy carried by the wave through a unit of surface, which is perpendicular to the propagation of the wave, and per unit of time. In short, the intensity of a wave is its power carried through a unit area.
The strength of sound waves is usually measured in decibels, which are based on a logarithmic scale, convenient for practical analysis of the results.
Intensity of various sounds
The following decibel scale gives an idea of the meaning of different sound intensities and the sensations that it causes:
- the threshold of unpleasant and uncomfortable sensations begins with 120 decibels (dB);
- a riveting hammer creates a noise of 95 dB;
- high-speed train - 90 dB;
- heavy traffic street - 70 dB;
- the volume of a normal conversation between people - 65 dB;
- a modern car moving at moderate speeds creates a noise of 50 dB;
- the average radio volume is 40 dB;
- quiet conversation - 20 dB;
- the noise of tree foliage - 10 dB;
- the minimum threshold for human sound sensitivity is close to 0 dB.
The sensitivity of the human ear depends on the frequency of sound and is the maximum value for sound waves with a frequency of 2000-3000 Hz. For sound in this frequency range, the lower threshold for human sensitivity is 10 -5 dB. Higher and lower frequencies than the indicated interval lead to an increase in the lower threshold of sensitivity in such a way that a person hears frequencies close to 20 Hz and 20,000 Hz only at their intensities of several tens of dB.
As for the upper threshold of intensity, after which the sound begins to cause inconvenience to humans and even pain, it should be said that it is practically independent of the frequency and lies in the range of 110-130 dB.
The geometric characteristics of the sound wave
A real sound wave is a complex oscillatory packet of longitudinal waves, which can be decomposed into simple harmonic vibrations. Each such oscillation is described from the geometric point of view with the following characteristics:
- Amplitude - the maximum deviation of each section of the wave from equilibrium. For this value, the designation A.
- Period. This is the time during which a simple wave makes its complete oscillation. After this time, each point of the wave begins to repeat its oscillatory process. The period is usually denoted by the letter T and measured in seconds in the SI system.
- Frequency. This is a physical quantity that shows how many vibrations a given wave makes in a second. That is, in its meaning, it is the inverse of the period. It is denoted by the Latin letter f. For the frequency of a sound wave, the formula for determining it through a period is as follows: f = 1 / T.
- The wavelength is the distance it travels over one period of oscillation. Geometrically, the wavelength is the distance between two nearest maxima or two nearest minima on a sine curve. The wavelength of sound waves is the distance between the nearest areas of air compression or the nearest places of its rarefaction in the space where the wave moves. It is usually denoted by the Greek letter λ.
- The speed of propagation of a sound wave is the distance over which the compression region or the region of rarefaction of the wave per unit time extends. This value is denoted by the letter v. For the speed of a sound wave, the formula has the form: v = λ * f.
The geometry of a pure sound wave, that is, a wave of constant purity, obeys a sinusoidal law. In the general case, the sound wave formula has the form: y = A * sin (ωt), where y is the coordinate value of a given point of the wave, t is time, ω = 2 * pi * f is the cyclic oscillation frequency.
Aperiodic sound
Many sound sources can be considered periodic, for example, sound from musical instruments such as a guitar, piano, flute, but there are also a large number of sounds in nature that are aperiodic, that is, sound vibrations change their frequency and shape in space. Technically, this kind of sound is called noise. Vivid examples of aperiodic sound are city noise, sea noise, sounds from percussion instruments, for example, from a drum and others.
Sound wave propagation medium
Unlike electromagnetic radiation, whose photons do not need any material medium for its propagation, the nature of sound is such that a certain medium is needed for its propagation, that is, according to the laws of physics, sound waves cannot propagate in a vacuum.
Sound can propagate in gases, in liquids, and in solids. The main characteristics of a sound wave propagating in a medium are as follows:
- the wave propagates linearly;
- it spreads equally in all directions in a homogeneous medium, that is, the sound diverges from the source, forming an ideal spherical surface.
- regardless of the amplitude and frequency of sound, its waves propagate at the same speed in a given environment.
The speed of sound waves in various environments
The speed of sound propagation depends on two main factors: the medium in which the wave moves, and the temperature. In general, the following rule applies: the denser the medium, and the higher its temperature, the faster the sound moves in it.
For example, the speed of sound wave propagation in air near the surface of the earth at a temperature of 20 ℃ and a humidity of 50% is 1235 km / h or 343 m / s. In water, at a given temperature, sound moves 4.5 times faster, that is, about 5735 km / h or 1600 m / s. As for the dependence of the speed of sound on temperature in air, it increases by 0.6 m / s with increasing temperature by every degree Celsius.
Timbre and tone
If you let the string or metal plate vibrate freely, it will produce sounds of different frequencies. It is very rare to find a body that makes a sound of one particular frequency, usually the sound of an object has a set of frequencies in a certain interval.
The timbre of sound is determined by the number of harmonics present in it, and their respective intensities. The timbre is a subjective quantity, that is, this is the perception of a sounding object by a specific person. The timbre is usually characterized by the following adjectives: high, brilliant, sonorous, melodic and so on.
Tone is a sound sensation that allows it to be classified as high or low. This value is also subjective and cannot be measured by any instrument. Tone is associated with an objective quantity - the frequency of a sound wave, but there is no unambiguous connection between them. For example, for a single-frequency sound of constant intensity, the tone increases with increasing frequency. If the sound frequency remains constant, but its intensity increases, then the tone becomes lower.
The shape of sound sources
In accordance with the shape of the body, which performs mechanical vibrations and thereby generates sound, the sources of sound waves are of three main types:
- Point source. It creates spherical sound waves that quickly decrease when moving away from the source (by about 6 dB if the distance from the source doubles).
- Linear source. It creates waves of a cylindrical shape, the intensity of which decreases more slowly than from a point source (with each double increase in the distance relative to the source, the intensity decreases by 3 dB).
- Flat or two-dimensional source. It generates waves only in a certain direction. An example of such a source would be a piston moving in a cylinder.
Electronic sound sources
To create a sound wave, electronic sources use a special membrane (speaker), which performs mechanical vibrations due to the phenomenon of electromagnetic induction. These sources include the following:
- players of various disks (CD, DVD and others);
- cassette recorders;
- radios;
- TVs and some others.