A sound wave is a wave process that occurs in gaseous, liquid and solid media, which, when it reaches the human hearing organs, is perceived by them as sound. The frequency of these waves lies in the range from 20 to 20,000 oscillations per second. We give formulas for a sound wave and consider its properties in more detail.
Why is there a sound wave?
Many people wonder what a sound wave is. The nature of sound lies in the occurrence of disturbances in an elastic medium. For example, when a pressure perturbation in the form of compression occurs in a certain volume of air, this area tends to spread in space. This process leads to compression of air in areas adjacent to the source, which also tend to expand. This process covers more and more of the space until it reaches some receiver, for example, the human ear.
General characteristics of sound waves
Let's consider what a sound wave is and how it is perceived by the human ear. Sound waveis longitudinal, when it enters the ear shell, it 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 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 perceive without harming it is 2800 µN/cm2. For comparison, let's say that the atmospheric pressure near the earth's surface is 10 million µN/cm2. Considering the proportionality of pressure and amplitude of oscillations, we can say that the latter value is insignificant even for the strongest waves. If we talk about the length of a sound wave, then for a frequency of 1000 vibrations per second, it will be a thousandth of a centimeter.
The weakest sounds create pressure fluctuations of the order of 0.001µN/cm2, the corresponding wave oscillation amplitude for a frequency of 1000 Hz is 10-9cm, while the average diameter of air molecules is 10-8 cm, that is, the human ear is an extremely sensitive organ.
The concept of the intensity of sound waves
With geometricFrom the point of view of a sound wave, it is a vibration of a certain form, from the physical point of view, the main property of sound waves is their ability to transfer energy. The most important example of wave energy transfer 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 a wave through a unit surface, which is perpendicular to the propagation of the wave, and per unit time. In short, the intensity of a wave is its power transferred 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 they evoke:
- threshold for unpleasant and uncomfortable sensations starts at 120 decibels (dB);
- riveting hammer generates 95 dB noise;
- high speed train - 90 dB;
- traffic street - 70 dB;
- the volume of a normal conversation between people is 65 dB;
- Modern car moving at moderate speeds generates 50 dB noise;
- average radio volume - 40 dB;
- quiet conversation - 20 dB;
- noise of tree foliage - 10 dB;
- The minimum human sound sensitivity threshold is close to 0 dB.
The sensitivity of the human ear depends onfrequency of sound and is the maximum value for sound waves with a frequency of 2000-3000 Hz. For a sound in this frequency range, the lower threshold of human sensitivity is 10-5 dB. Higher and lower frequencies than the specified interval lead to an increase in the lower sensitivity threshold in such a way that a person hears frequencies close to 20 Hz and 20,000 Hz only at their intensity of several tens of dB.
As for the upper threshold of intensity, after which the sound begins to cause inconvenience for a person and even pain, it should be said that it practically does not depend on frequency and lies in the range of 110-130 dB.
Geometric characteristics of a sound wave
A real sound wave is a complex oscillatory package of longitudinal waves, which can be decomposed into simple harmonic vibrations. Each such oscillation is described from a geometric point of view by 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 it takes for a simple wave to complete 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 oscillations a given wave makes per second. That is, in its meaning, it is a value inverse to 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 length of a wave is the distance it travels in one period of oscillation. Geometrically, wavelength is the distance between two nearest maxima or two nearest minima on a sinusoidal curve. The oscillation length of a sound wave 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 sound wave propagation is the distance over which the area of compression or the area of rarefaction of the wave propagates per unit of time. This value is denoted by the letter v. For the speed of a sound wave, the formula is: v=λf.
The geometry of a pure sound wave, that is, a wave of constant purity, obeys a sinusoidal law. In the general case, the formula of a sound wave is: y=Asin(ωt), where y is the value of the coordinate of a given point of the wave, t is time, ω=2pif is the cyclic oscillation frequency.
Aperiodic sound
Many sound sources can be considered periodic, for example, the sound from musical instruments such as 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. brightexamples of aperiodic sound are urban noise, the sound of the sea, sounds from percussion instruments, such as a drum, and others.
Sound propagation medium
Unlike electromagnetic radiation, whose photons do not need any material medium for their 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 vacuum.
Sound can travel through gases, liquids and solids. The main characteristics of a sound wave propagating in a medium are as follows:
- wave propagates linearly;
- it spreads equally in all directions in a homogeneous medium, that is, sound diverges from the source, forming a perfect spherical surface.
- regardless of the amplitude and frequency of sound, its waves propagate at the same speed in a given medium.
The speed of sound waves in various media
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 propagation speed of a sound wave in the air near the earth's surface 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 travels 4.5 times faster, thenthere is about 5735 km/h or 1600 m/s. As for the dependence of the speed of sound on the temperature in the air, it increases by 0.6 m/s with an increase in temperature for every degree Celsius.
Timbre and tone
If a string or metal plate is allowed to vibrate freely, it will produce sounds of different frequencies. It is very rare to find a body that would emit a sound of one particular frequency, usually the sound of an object has a set of frequencies in a certain interval.
The timbre of a sound is determined by the number of harmonics present in it and their respective intensities. Timbre is a subjective value, that is, it is the perception of a sounding object by a specific person. 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 relationship between them. For example, for a single-frequency sound of constant intensity, the tone rises as the frequency increases. If the frequency of the sound remains constant, but its intensity increases, then the tone becomes lower.
Shape of sound sources
According to the shape of the body that vibrates mechanically and thereby generates sound, there are three main types of sources of sound waves:
- Point source. It produces sound waves that are spherical in shape and decay rapidly with distance from the source (approximately 6dB if the distance from the source is doubled).
- Line source. It creates cylindrical waves whose intensity decreases more slowly than from a point source (for each doubling of the distance from the source, the intensity decreases by 3 dB).
- A 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 for various discs (CD, DVD and others);
- cassette recorders;
- radios;
- TVs and some others.
