SHM, WAVE MOTION & SOUND

WAVE MOTION

Can transfer energy and information

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They involves vibrations (OSCILLATION)

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Wave length

FREQUENCY(F) is number of waves in one second

The distance between two successive crests or troughs of a wave

Measured in Hertz( Hz)

50 Hz = 50 vibrations in one second

Distance between two peeks troughs measured in LAMBDA

Wave speed

speed

distance/time

wavelength/time

period=time

wavelength=distance

Formula

V

Frequency x λ

λ / period

Reflection of waves

Open boundary

When a wave strikes an interface in case of open boundary it will get reflected as well as refracted.

Closed boundary

When a wave is incident on an interface it will completely get reflected

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SOUND

SPEED OF SOUND WAVES

SOUND WAVES

Fundamentals of sound wave

wavelength is distance between each successive region of high or low pressure

sound is simply any longitudinal wave in a medium

frequency is number of oscillations in pressure per second

molecules in the air vibrate about the same average position creating the compressions and refractions. It is called the frequency of sound the pitch.

also can be described by : image-4

Amplitude of a sound wave

Periodic+Sound+Waves+_+the+gas+pressure+measured+from+the+equilibrium+value.+_+pressure+amplitude.

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Perceptions of sound waves

the harmonic content greatly affects our perception of sound image-7

depends on the characteristics of the medium. Table+16.1_+Speed+of+sound+in+various+bulk+materials

the speed of sound in fluid

the speed depends on the fluid's compressibility and inertia

the speed of sound in solid

sound travels faster in solids than in fluids and gases

the speed of sound in gases

sound travels slowest through gases

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SOUND INTENSITY

the sound power as it passes through a given area

I=P/A (W/m^2)

the loudness or volume of the sound.

the greater the amplitude of the fluctuations in the pressure, the louder the sound appears.

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the intensity of a sinusoidal sound wave is proportional to the square of the amplitude, the square of the frequency, and the square of the pressure amplitude.

intensity is proportional to 1/r^2 when the sound source emits waves in all directions equally.

but intensity DECREASES with distance more slowly than 1/r^2 when the sound goes predominantly in one direction.

we can measure the sound intensity

units of sound level intensity: decibels (dB), a logarithmic scale.

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STANDING SOUND WAVES AND NORMAL MODES

a pressure node is always a displacement antinode, and a pressure antinode is always a displacement node

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sound waves in organ pipes

different sizes produce tones with different frequencies

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harmonics in an open pipe

an open pipe is open at both ends

harmonics in a closed pipe

a closed pipe is open at one end and closed at other end

RESONANCE AND SOUND

resonance is when the frequency of a forced vibration matches the object's natural frequency

a dramatic INCREASE in amplitude occurs

Resonance+and+sound

INTERFERENCE OF SOUND

the difference in the lengths of the paths traveled by the sound determines whether the sound from two sources interferes constructively or destructively.

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constructive interference results in antinodes and occurs whenever a thick line meets a thick line.

thus listeners at the antinodes hear the sound from the sources better than listeners at the
nodes.

BEATS

when two or more waves superimpose each other with slightly different frequencies, then a sound of periodically varying amplitude at a point is observed.

the number of amplitude maxima per second is called beat frequency.

if we have two sources, their difference in frequency gives the beat frequency

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DOPPLER EFFECT

refers to the change in frequency when there is relative motion between an observer of waves and the source of the waves

doppler shift is change in sound frequency due to the relative motion of either the source or the detector

example: a passing car

you hear the high pitch of the siren of the approaching ambulance, and notice that its pitch drops suddenly as the ambulance passes.

it is called doppler effect.

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an approaching source moves closer during period of the sound wave so the effective wavelength is shortened

giving a higher pitch since the velocity of the wave is UNCHANGED. Similarly the pitch of a receding sound source will be lowered.

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change in wavelength doppler effect

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SHOCK WAVES

a sonic boom occurs if the source is supersonic

an aircraft travelling through the atmosphere continously produces air-pressure waves similar to the water waves caused by a ship's bow

when the aircraft exceeds the speed of sound, these pressure waves combine and form visible shock waves

supersonic is faster than the speed of sound

the angle alpha is given by sin alpha equals to v over vs, where v over vs is called the Mach number

Mach number is speed of object over speed of sound

produced by supersonic aircraft, three-dimensional cone shaped

sonic boom is sharp crack heard when conical shell of compressed air that sweeps behind a supersonic aircraft reaches listeners on the ground

diffraction and sound involves a change in direction of waves they pass through an opening or around a barrier in their path

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PHYSICS AND MUSIC

for the music folks

fundamental and harmanics dissonance and consonance

music vs noise

most pieces of music set up a limited amount of dissonance on purpose and then resolve it to a consonant conclusion.

noise contains a great deal of dissonance and provides no relief.

three ways to distinguish sounds physically

intensity is interpreted by the human brain as loudness

frequency is interpreted by the human brain as pitch

harmonic content is interpreted by the human brain as a component of the timbre

TIMBRE: SOUND QUALITY

the characteristics of a sound which allow the human to distinguish between sounds of the same pitch and loudness

there are three contributors to timbre

attack and decay

vibrato/tremolo

harmonic content (the most IMPORTANT contributor)

describes how quickly the amplitude of the sound reaches a maximum and how quickly it dies out

vibrato is periodic changes in the pitch of the tone. It is called frequency modulation of tone

tremolo is used to indicate periodic changes in the amplitude or loudness of the tone. It is called amplitude modulation of tone

SIMPLE HARMONIC MOTION

certain kind of oscillatory, or a wave-like motion that describes the behaviour of many physical phenomena

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pendulum

Low amplitude waves in air(sound), water & ground

Electromagnetic field of laser light

Vibration of a plucked guitar string

Electric current of most AC power supplies

Total energy of oscillating system constant

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Potential energy, U

Kinetic energy, K

Total energy, E

Graph of:

Energy variation with displacement, 1

Energy variation with time, 2

Damped Oscillation

When amplitude decreasing with time

Light Damping : Amplitude of oscillation slowly goes down with the period of oscillation remaining the same.
(e.g simple pendulum)

Hard Damping : Amplitude of the spring goes down without further oscillation and become stationary.
(e.g A spring inside a highly viscous oil)

Critical Damping : Amplitude rapidly goes down, then without shooting up it becomes stationary. (e.g Car suspension system)

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Spring Block System

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Equation of SHM:

Displacement, shm-10-728 (2)

Velocity, physics-chapter-9simple-harmonic-motion-10-728 (2)

Acceleration, physics-chapter-9simple-harmonic-motion-10-728 (3)

Kinetic energy, physics-chapter-9simple-harmonic-motion-10-728 (4)

Potential energy, physics-chapter-9simple-harmonic-motion-10-728 (5)