# How far do sound waves travel

## Acoustics

The essentials in brief...

Mechanical vibrations in the audible frequency range from 16 Hz to 20 kHz are called sound.
What is sound - a definition

In order for sound to propagate, a transmission medium must be available (gas, liquid or solid). A distinction is made between airborne noise, liquid-borne noise and structure-borne noise.
Sound transmission and types of sound

The propagation of sound in the air occurs through the movement of gas molecules, which transmit a pressure difference and in this way transmit a signal.
How does sound actually come about?

The rapid air pressure fluctuations that we perceive as sound are only around 0.05 Pa (1 / 2,000,000 of the atmospheric pressure) in a normal conversation.
Sound pressure and sound pressure level

Sound propagates as a longitudinal wave in a medium. The particles of the medium move around their position of rest due to the sound wave, but they are not transported with the wave. Sound waves transport energy and information, but not matter!
What is a wave

The frequency f [Hz] indicates how many wavelengths (periods) are passed through in one second. The following applies: frequency = speed of sound / wavelength. Sound travels at different speeds in different materials. The speed of sound in the air is 340 meters per second.
Frequency, wavelength, amplitude and speed of sound

The frequency determines the pitch, the amplitude the sound pressure (and thus also the volume).
Frequency and amplitude increase

When an ambulance with a siren moves towards us, the frequency increases and with it the pitch. As it moves away, the frequency drops.
The Doppler Effect

### What is sound - a definition

Sound is understood to mean mechanical vibrations in a gaseous, liquid or solid substance with frequencies in the audible range of the human ear. The frequency reflects the number of oscillations of the sound wave per second, measured in Hertz [Hz]). The human hearing range is between 16 Hz and 20,000 Hz, with the upper limit decreasing with increasing age towards lower frequencies, meaning that adults are usually more difficult to perceive high tones than children.

Sound waves with frequencies below 16 Hz are referred to as infrasound, those with a number of vibrations in excess of 20,000 vibrations per second are referred to as ultrasound. These areas, which are inaudible to humans, are perceived by some animal species and used for communication or orientation. Bats can orientate themselves very well even at night thanks to the ultrasonic echo sounder. Some species of whale are known to be able to communicate over distances of several kilometers using infrasound. The roar of tigers also contains an inaudible portion in the infrasound range that is inaudible to humans, which can be heard by conspecifics up to eight kilometers away.

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### Sound transmission and types of sound

In contrast to electromagnetic waves such as light, microwaves and radio waves, sound waves cannot propagate in a vacuum. Sound waves need what is known as a transmission medium made up of moving particles that transmit the wave. Such a medium are, for example, air, water, masonry or iron. Humans are mainly used to sound transmission through the air: when speaking, listening to music, the purring of the PC fan, etc.

 Source: Booklet "Humorous Noise Abatement" The transmission of sound waves through the air is known as airborne sound. A distinction is made between direct and indirect sound. Direct sound arrives directly at the receiver without reflections. Indirect sound describes sound waves that have been reflected at least once from an object on their way to the receiver.

Mechanical vibrations that propagate in solid materials are referred to as structure-borne noise. Structure-borne sound cannot be perceived by the ear. However, it is converted into airborne sound by radiation from walls, floors and other surfaces, which the ear perceives. The surface behaves like the movable membrane of a loudspeaker and thereby sets the air vibrating (even a thick wall can vibrate). Examples of structure-borne noise are: hammering, dropping objects, walking on the floor or stairs (which is referred to as impact noise in building acoustics).

 Source: Booklet "Humorous Noise Abatement" Structure-borne noise describes the mechanical vibrations that propagate in solid materials. A special type of structure-borne sound is the so-called impact sound (right)

Combined sound transmission also often occurs. In the case of bowed and plucked instruments, a string is made to vibrate, which transmits these vibrations to the resonance body via structure-borne sound. The air is then stimulated in and around the resonance body, which finally carries the sound to our ears.

 Source: Booklet "Humorous Noise Abatement" A combination of structure-borne sound and air-borne sound is often responsible for the characteristic sound of musical instruments (e.g. drum, violin). The construction also has an influence on the volume that can be generated and, above all, on the timbre.

The lack of a transmission medium means that it is absolutely still in the almost particle-free space! If this were not the case, we would not only be able to see the sun, but also hear the huge eruptions on the surface!

 Sun surface with huge eruptions (protuberances). The interstellar space is almost completely empty. The sound transmission medium is missing, so it is absolutely silent. If a transmission medium were available, one could not only see the active solar surface, but also hear it. Source: http://npf-geofizika.ru/ leuza / kosmos.htm

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### How does sound actually come about?

Sound is created by the compression or expansion of matter, caused by the movement of an adjacent surface (e.g. air, with a loudspeaker membrane). The particles of matter are briefly pressed closer against each other in a certain area around the sound source, which results in a pressure difference to the environment. The particles try to reduce this pressure difference by in turn "pressing" on the neighboring particles. The same thing happens to these neighbors as before to the particles in the membrane. In turn, they pass on the pressure difference. So a pressure difference (disturbance) propagates through the medium like waves. The greater the movement resp. Disturbance at the beginning, the greater the so-called sound pressure. Depending on the medium, the particles are atoms or molecules. Since our ambient air consists of around 78% nitrogen and 21% oxygen, it is mainly the nitrogen and oxygen molecules that can form a sound wave in the air.

 Source: www.kemt.fei.tuke.sk/Predmety/KEMT320_EA/_web/ Online_Course_on_Acoustics / Sound propagation in the air occurs through the movement of the gas molecules, which pass on the pressure difference and thus transmit a signal. The greater the amplitude, the greater the sound pressure and the more energetic the sound wave.

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### Sound pressure and sound pressure level?

The audible pressure fluctuations are tiny compared to the atmospheric pressure. In physical terms, they are superimposed on the prevailing air pressure and are referred to as sound pressure. The abbreviation for sound pressure is P and the unit is Pascal [Pa]. A normal conversation causes pressure fluctuations of approx. 0.05 Pa, which corresponds to around 1 / 2,000,000 of the atmospheric pressure.

However, changes in the weather cause the air pressure to fluctuate by several thousand Pa within days! Even when climbing stairs, the difference in height causes pressure fluctuations of several tens of Pa. However, these pressure changes are very slow compared to the pressure changes of sound waves. That is why our hearing is designed to only register the rapid fluctuations in air pressure.

To achieve this, nature has come up with a simple but ingenious trick: The air pressure on the inside of the eardrum is constantly adjusted to the prevailing pressure on the outside of the eardrum. This pressure equalization between the outside and inside takes place via the so-called Eustachian tube. When yawning or other jaw movements, this connection between the pharynx and the middle ear is opened and the pressure is equalized.

The existing static air pressure acts equally on the outside and inside of the eardrum. Therefore it has no influence on hearing.

Since the sound pressure of a tone is so small, the sound pressure of a tone is compared with the pressure of a barely perceptible tone at 1000 Hz to indicate the strength of the sound. This relative reference is called the sound pressure level L, or sound level for short. The dimensions are given in decibels [dB] (more on this in the section "Sound level, volume and sound measurement").

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### What is a wave

Everyone has watched the waves that occur when you throw a stone into the water.

 Source: http://www.fh-augsburg.de/ ~ clemen / lehre / few / few_start.htm

On the surface, waves propagate in concentric circles around the origin of the disturbance. It is similar with sound waves in the air. A periodic pattern of wave crests and troughs is characteristic of a wave. Mathematically, a wave can be elegantly described with a sine or cosine curve. When the particles move back and forth in the direction of propagation of a wave, one speaks of longitudinal waves. These types of waves are responsible for the transmission of sound in the air. In liquids and solids, another type of wave can also occur in which the particles move back and forth perpendicular to the direction of propagation. This wave propagation is then called transversal.

Source: "moving acoustics" program, Chalmers Vibroacoustic Group

Longitudinal and transverse wave propagation in comparison. The waves run from left to right in both examples. In the case of the longitudinal waves, the vertical alignment of the particles does not change. The red rectangle is only compressed and stretched horizontally. In the case of the transverse wave, on the other hand, the forces occur transversely to the direction of wave propagation. In both cases, the particles are excited to move by the wave, but they are not transported with the sound wave.

It is important that the particles themselves do not move with the wave, they only move back and forth around their mean position of rest. They say they oscillate. The particles do not move at the same speed as the sound wave. So the wave does not transport matter, but energy and information. By changing the frequency or amplitude of waves, data can be sent to a receiver with the waves. If this data makes sense through interpretation, it is called information. This is the basis for telecommunications.

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### Frequency, wavelength, amplitude and speed of sound

If air is set in regular vibrations by an instrument or a machine, these vibrations spread out as sound waves. The time it takes for the oscillation to repeat itself is called the period or duration of oscillation and is often referred to as T. The number of oscillations (periods) per second is called frequency f and is denoted by the unit Hertz [Hz] = [1 / s].

The frequency thus corresponds to the reciprocal of the period: f = 1 / T. For all types of waves, the following relationship between frequency, speed of propagation and wavelength applies:

The speed of propagation, i.e. the speed at which the wave moves through the medium, is with c and specified in [m / s]. Sound moves through air at around 343 m / s (1,234 km / h) at 20 ° C. In water, at 10 ° C, the speed of sound is 1,440 m / s, which is more than four times as great as in air. The speed of sound in a certain medium has to do with its density and the mobility of the particles. The speed of sound is therefore very different depending on the propagation medium. The length of a full oscillation is called the wavelength. It corresponds to the distance between two successive wave crests and is measured in meters [m].

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### Frequency and amplitude increase

The maximum deflection of the particles from their middle position, i.e. the height of a wave crest or the depth of a wave trough, is called amplitude. The size of the amplitude determines the energy content and the associated volume of a signal. The frequency, on the other hand, is responsible for the pitch. The higher the frequency, the shorter the period of oscillation and the higher the tone.

Source: SuvaPro "Audio Demo 3" documentation

Increase in amplitude at constant frequency.
The greater the amplitude, the louder the signal.

Source: SuvaPro "Audio Demo 3" documentation

Frequency increase with constant amplitude.
The higher the frequency, the higher the tone.

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### The Doppler Effect

The Doppler effect does not mean twice, but speaks of a fact that the Austrian Christian Doppler discovered more than 150 years ago. He was concerned with the question: What does a sound sound like when a sound source is moved away from us? Is this tone higher, lower or the same?

When a honking car or an ambulance moves towards us, the frequency increases and with it the pitch. As it moves away, the frequency drops. The faster the sound source moves relative to the observer, the more pronounced the effect. This phenomenon is called the Doppler effect.

Effects of sound propagation

#### Doppler effect

Car driving by quickly, honking its horn

The horn has a frequency of approx. 1000 Hz. In the example here, the frequency in our ear increases to 1115 Hz (the car is moving towards us) and then drops to 951 Hz (the car is moving away).

#### stationary sound source

The sound propagation occurs spherically symmetrically to the stationary center and results in the same pitch everywhere for a stationary observer.

#### Sound source in motion

The sound propagates spherically symmetrically, but because of the movement of the center there are direction-dependent differences in the pitch.

#### «Sound barrier», the speed of sound

A US Air Force jet breaks the sound barrier

Favorable conditions make the "sound barrier" resp. the enormous pressure differences are visible.

#### Supersonic and Mach cone

A bullet at supersonic speed.

The clearly visible shock wave is called Mach'scher Cone.

Source moves at Mach 0.7
Source moves at Mach 1.0
Source moves at Mach 1.4

Swell:
Animations / pictures Doppler effect: http://www.gmi.edu/~drussel
Audio sample: SuvaPro Audio Demo 3

### Explanation of the Doppler effect

Imagine that the perceived frequency corresponds to the number of sound waves that reach your ear per second. The horn in the example has a frequency of around 1000 Hz, which means it emits 1000 sound waves per second. These now whiz through the air at a speed of 340 m / s and reach your ear after a short time. If the horn moves towards you, you will reach more sound waves per second, the frequency increases in this example to 1115 Hz. Conversely, the frequency decreases to 951 Hz when the horn moves away from you.

### To confusion

When calculating the frequency, it depends on whether the transmitter or the receiver is moving. This probably contradicts your ideas about relativity. If you move away from a sound source at the speed of sound, you will no longer hear anything from the sound source. However, if the sound source moves away from you at the speed of sound, you will still hear the sound, but only at half the frequency.

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