The physics of soundClil module for IV D s - a.s. 2009/2010

Wave: definition

a wave is a disturbance or variation which travels through a medium

the particles in the medium do not travel with the wave

the particles oscillate around an equilibrium point

energy is transferred through the medium from the source of the wave

Mathematical description of waves

Period: the time required to complete a full cycle, T in seconds

Frequency: the number of cycles per second, f in 1/seconds or Hertz (Hz)

Amplitude: the maximum displacement from equilibrium A

Velocity of propagation: v

Wavelength: the distance which a disturbance travels along the medium in one complete wave cycle , λ in m.

Longitudinal vs Transverse waves

Transverse wave

Longitudinal wave

Sound waves

Sound is a mechanical wave: such waves require a material medium.

Sound is a longitudinal mechanical wave that originates from a mechanical vibration (source) and propagates in an elastic material medium (usually air).

“In Space, No One Can Hear You Scream”

Sound waveThe sound wave is moving through air, then as one air particle is displaced from its equilibrium position, it exerts a push or pull on its nearest neighbors, causing them to be displaced from their equilibrium position. This particle interaction continues throughout the entire medium, with each particle interacting and causing a disturbance of its nearest neighbors.

The result of such longitudinal vibrations is the creation of compressions and rarefactions within the air.

MECHANICAL WAVE

Sound waveThe compressions are regions of high air pressure while the rarefactions are regions of low air pressure.

The wavelength of a wave is commonly measured as the distance from one compression to the next adjacent compression or the distance from one rarefaction to the next adjacent rarefaction.

Sound propertiesFREQUENCY. The frequency of a wave refers to how often the particles of the medium vibrate when a wave passes through the medium. The frequency of a wave is measured as the number of complete back-and-forth vibrations of a particle of the medium per unit of time;

The frequency of a sound wave not only refers to the number of back-and-forth vibrations of the particles per unit of time, but also refers to the number of compressions or rarefactions which pass a given point per unit of time

Sound properties

Human ear is capable of detecting sound waves with a wide range of frequencies, ranging between approximately 20 Hz to 20 000 Hz

The sensation of a frequency is commonly referred to as the pitch of a sound. A high pitch sound corresponds to a high frequency sound wave and a low pitch sound corresponds to a low frequency sound wave

Sound intensityThe amount of energy which is transported past a given area of the medium per unit of time is known as the intensity of the sound wave. The greater the amplitude of vibrations of the particles of the medium, the greater the rate at which energy is transported through it, and the more intense that the sound wave is. Intensity is the energy/time/area; and since the energy/time ratio is equivalent to the quantity power, intensity is simply the power/area.

Typical units for expressing the intensity of a sound wave are:

Watts/meter2.

Sound intensityHumans are equipped with very sensitive ears capable of detecting sound waves of extremely low intensity. The faintest sound which the typical human ear can detect has an intensity of 1*10-12 W/m2. A sound with an intensity of 1*10-12 W/m2 corresponds to a sound which will displace particles of air by a mere one-billionth of a centimeter.

This faintest sound which a human ear can detect is known as the threshold of hearing

The most intense sound which the ear can safely detect without suffering any physical damage is more than one billion (109) times more intense than the threshold of hearing.

Sound Intensity

The scale which is frequently used by physicists to measure intensity is a scale based on multiples of 10. This type of scale is called a logarithmic scale. The scale for measuring intensity is the decibel scale. The threshold of hearing is assigned a sound level of 0 decibels (0 dB); this sound corresponds to an intensity of 1*10-12 W/m2. A sound which is 10 times more intense ( 1*10-11 W/m2) is assigned a sound level of 10 dB. A sound which is 100 times more intense ( 1*10-10 W/m2) is assigned a sound level of 20 db.

Sound intensity

If one sound is 10x times more intense than another sound, then it has a sound level which is 10*x more decibels than the less intense sound.

Sound intensityWhile the intensity of a sound is a very objective quantity which can be measured with sensitive instrumentation, the loudness of a sound is more of a subjective response which will vary with a number of factors. The same sound will not be perceived to have the same loudness to all individuals.

Two sounds with the same intensity but different frequencies will not be perceived to have the same loudness. Because of the human ear's tendency to amplify sounds having frequencies in the range from 1000 Hz to 5000 Hz, sounds with these intensities seem louder to the human ear

Timbre

Sounds may be generally characterized by pitch, loudness (or intensity), and timbre

timbre describes those characteristics of sound which allow the ear to distinguish sounds which have the same pitch and loudness

TimbreTimbre is mainly determined by the harmonic content of a sound and the dynamic characteristics of the sound such as vibrato and the attack-decay envelope of the sound.

Harmonic content determines the waveform of the sound signal when displayed as a function of time

Sound PropagationAs for any other waves, you can observe the following behaviour of sound waves:

when a longitudinal sound wave strikes a flat surface, sound is reflected (Reflection)

When sound waves enter a medium where their speed is different the travelling direction changes (Refraction)

Sound waves bend around small obstacles and they spread out beyond small openings (Diffraction).

Sound Propagation

Resonance

In sound applications, a resonant frequency is a natural frequency of vibration determined by the physical parameters of the vibrating object. This same basic idea of physically determined natural frequencies applies throughout physics in mechanics, electricity and magnetism.

ResonanceResonance requires 3 basic conditions:

A) An Object With a Natural Frequency: The object can be a mechanical device or an electronic circuit. An object's natural frequency is the frequency it tends to oscillate at when disturbed.

The oscillation can be a mechanical vibration as is the case when the string of a guitar is strummed. An object can have more than one natural frequency. These are called harmonics. A guitar string sounds musical because it vibrates with several harmonics when it is strummed.

Resonance

B) A Forcing Function at the Same Frequency as the Natural Frequency: In mechanical systems the forcing function is a variable force. In electronic circuits it arises from a variable electric field. In either case the forcing function does work on the object it is applied to. Since work is a form of energy transfer it causes energy to build up in the object.

C) A Lack of Damping or Energy Loss: For an object to resonate, mechanical or electrical energy has to build up in the object. Anything which removes these forms of energy tends to interfere with resonance. Friction, air resistance, and viscous drag can all provide damping in mechanical systems.

ResonanceWhen the forcing function's frequency  matches the natural frequency of an object it will begin to resonate. The forcing function adds energy at just the right moment during the oscillation cycle so that the oscillation is reinforced. This makes the oscillation's amplitude grow larger and larger. These oscillations would eventually become infinitely large. However, as mentioned earlier, long before the oscillations reach infinity one of three things happens:

1) the object's dynamics change so that the resonant frequency and forcing functions no longer match,

2) the energy lost as heat, sound, or light becomes equal to the energy input.

3) the object breaks