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Sound

Sound is a longitudinal wave. When a sound is produced by friction, impact or vibration of a material, a compression wave passes through a medium. This medium could be solid, liquid or gas.

Speed of Sound

The speed of a sound wave does not depend on the amplitude, frequency or wavelength of the sound wave, but on the characteristics of the medium it is passing through. In air, sound speed will vary according to pressure (altitude), humidity and temperature. The speed of sound in air is about 340m/s at sea level and S.T.P.

vsound = 340m/s

Sound has different speeds in different mediums. In water it is about 1500 m/s. In iron 5120 m/s.

C note frequencies
The note C doubles in frequency with every octave

Pitch and Intensity

Our ears always hear sound at the same speed in air. So how is it that music can be so different in volume and pitch?

Sound is produced by anything that causes air to be disturbed. The beating of a drum causes a wave to travel across the drum skin to to the edges, where it reflects. If the skin is made tauter (pulled tight), the frequency increases. This is because the wave can pass more quickly when the particles of the skin have less room to move, and so absorb less of the energy of the wave.

The same thing happens when a guitar string is plucked, or a piano note is played. A wave travels along the string and reflects from the end. The frequency of the note played depends on the length of the string. The shorter the string, the shorter the wavelength. Since the wavelength and frequency are inversely proportional (remember, v = f⋅λ), as the wavelength decreases, the frequency increases. As the string is shortened, by the guitarist pressing down on a fret (a ridge along the fingerboard), preventing the string from vibrating along its full length, the sound goes up in pitch (increases frequency).

Harmonics

Harmonics
Harmonics are whole number multiples of wavelengths within the base, or fundamental wavelength

Music works by combinations of these waves. But, some notes that are close together, such as two adjacent keys on a piano, sound awful when played together. Why is that?

The answer lies in harmonics. Harmonics is simply 'how harmonious' two sounds are. In terms of physics, it is a question of how many wavelengths there are - if one note has exactly twice as many waves per second (twice the frequency) as another wave, then exactly two waves are heard from the first note while one wave is heard from the second. The waves 'add together' at the ear, and the result is 'constructive interference'. This sounds pleasant, because the waves are adding their energies in a harmonious way.

However, if two waves have wavelengths that are not multiples of each other, the sound at the ear has a conflict, and the resultant sound is unpleasant.

Sound patterns match, or fit together, when an exact number of wavelengths fit inside a long fundamental wavelength. This is why the clarinet, for example, can make three 'octaves' without changing the length of the instrument.

Sound Intensity

The lowest intensity which the human ear can detect is $I_0 = 1.0 x 10^{-12}$ W $m^-1$.<(p>

The decibels scale measures intensities of sound relative to this base intensity, but on a logarithmic scale.

$Δβ ∝ {ΔI}/I$ (Weber-Frechner law), where Δβ is a factor related to the human perception of hearing.

Since the human ear perceives sound in a logarithmic way, we can express β more meaningfully in dB (decibels):

$β = 10log(I/{I_0})$ dB

Decibel scale of sound intensity

Sound emitterIntensity (dB)Pressure (Pa)
Hearing threshold00.00002
Library400.002
TV room700.06
City street800.2
Rock concert1106
Pain threshold12020
Construction tools13060
Jet taking off140200

Ultrasound

The human ear can detect sound with frequencies between about 20 Hz to 20 kHz. The range above this is known as ultrasound. Dogs can hear all our frequencies and up to about 50 kHz, while bats can hear as far as 120 kHz!

Ultrasound is a longitudinal wave. It is used in medicine, in engineering, and for detecting objects under water.

Medicine

Ultrasound in concentrated beams is used to break up kidney and gall stones, without the need for surgery. Women can see their babies in the womb with ultrasound, and some therapies use ultrasound to massage muscles or cause substances to pass through tissues easily.

Engineering

Delicate instruments and machinery can be cleaned by ultrasound vibrations in a bath of solvent. Defects or breaks in metal show up in ultrasound scans of metal. The navy seek out enemy submarines, and deep-sea salvage companies can detect submerged objects with echo-sounders, which send energetic pulses of sound in the ultrasound range.

Content © Andrew Bone. All rights reserved. Created : January 13, 2014

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