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
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 :
Amplitude of a sound wave
Perceptions of sound waves
the harmonic content greatly affects our perception of sound
depends on the characteristics of the medium.
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
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.
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.
STANDING SOUND WAVES AND NORMAL MODES
a pressure node is always a displacement antinode, and a pressure antinode is always a displacement node
sound waves in organ pipes
different sizes produce tones with different frequencies
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
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.
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
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.
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.
change in wavelength doppler effect
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
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,
Kinetic energy,
Total energy,
Graph of:
Energy variation with displacement,
Energy variation with time,
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)
Spring Block System
Equation of SHM:
Displacement,
Velocity,
Acceleration,
Kinetic energy,
Potential energy,