fundamentals of sound

ANY BACK AND FORTH MOVEMENT BETWEEN 2 STATES

AN OSCILLATION THAT IS MECHANICAL, WITH ELASTICITY ACTING AS THE RESTING FORCE.

COMMONLY USED AS A MODEL OF MOTION. MUST BE DISPLACED BY AN EXTERNAL FORCE IN ORDER FOR IT TO MOVE.

ALL OSCILLATIONS ARE NOT VIBRATIONS BUT ALL VIBRATIONS ARE OSCILLATIONS

RESISTANCE TO AN OBJECT TO CHANGE IT'S STATE OF MOTION.

• HAS POTENTIAL ENERGY
• KINETIC HAS TO DO WITH MOVEMENT OR MOTION DUE TO AN OBJECTS VELOCITY

GIVES A PENDULUM POTENTIAL ENERGY

• IS A VECTOR QUANITY THAT IS DESCRIBED BY ITS MAGNITUDE AND ITS DIRECTION.
• DIRECTION: RIGHT IS POSITIVE
• LEFT IS NEGATIVE

BACK AND FORTH MOTION OF A PENDULUM IS CALLED A SINUSOIDAL MOTION OR A SINE WAVE

RATE OF CHANGE AND DISPLACEMENT

RATE OF CHANGE IN VELOCITY

• POSITIVE: OBJECT IS ACCELERATING FROM THAT POINT TO THE POSITIVE DIRECTION
• NEGATIVE: OBJECT IS ACCELERATING FROM THAT POINT TO THE NEGATIVE DIRECTION

PERIODIC: MOTION THAT REPEATS ITSELF IN REGULAR INTERVALS UNTIL IT IS STOPPED BY EXTERNAL ACTION.

HARMONIC: MOTION IN WHICH THE ACCELERATION OF THE OBJECT IS DIRECTLY PROPORTIONATE BUT OPPOSITE IN DIRECTION TO THE DISPLACEMENT OF THE OBJECT FROM ITS EQUILIBRIUM POSITION.

• SIMPLE HARMONIC MOTION OR SINUSOIDAL MOTIO OCCURS WHEN THE MOTIO OF A SINGLE OBJECT:
• ***HAS AN ACCELERATION THAT IS DIRECTLY PROPORTIONAL BUT OPPOSITE IN DIRECTION TO THE DISPLACEMENT

AND

CHANGES IN DISPLACEMENT, VELOCITY, AND ACCELERATION ARE SINUSOIDAL FUNCTIONS OF TIME.

A FUNCTION REPRESENTING CHANGES IN PHYSICAL QUANTITY AS A FUNCTION OF TIME.

• FREQUENCY = NUMBER OF CYCLES PER SECOND
• (f)
• MEASURED IN HERTZ (HZ) OR CYCLES PER SECOND (CPS)
• 1 CYCLE/SECOND = 1 HZ

ONE FULL REPETITION OF MOTION

• TIME REQUIRED TO COMPLETE ONE CYCLE (T)
• REPORTED IN A TIME UNIT SUCH AS SECONDS (S)
• MILLISECONDS (MS) OR MICROSECONDS (μs)
• *INVERSE RELATIONSHIP BETWEEN FREQUENCY (F) AND PERIOD (T)

#CYCLES/SECONDS = FREQUENCY

TIME/# OF CYCLES=PERIOD

• 1. (T) = .00025
• 2. (F) = 1/.002 = 500
• 3. (T) =1/40 = .025
• 4. (F) 1/1= 1HZ

EXTRA NOTE: 1MS=.001

• phase angle between twowaves is a measure of their difference in phase.
• Two wavesof the same frequency that are perfectly in phase have phaseangle zero;
• if one wave is ahead of the other by a quartercycle, its phase angle 90 degrees (π/2 radians);
• waves thatare perfectly out of phase have phase angle 180 degrees (πradians), and so on.

• IN PHASE- HAVE SAME STARTING POINT ON WAVEFORM
• OUT OF PHASE HAVE DIFFERENT STARTING POINT ON WAVEFORM

• MAXIMUM POSSIBLE VALUE IS 180
• CAN BE DETERMINED BASED ON ANY TIME POINT
• REPORTED AS A POSITIVE NUMBER
• PHASE DIFF ALWAYS POSITIVE

• CAN BE POSITIVE OR NEGATIVE
• DIRECTION DEPENDS ON WHICH WAVEFORM IS DESIGNATED AS THE PRIMARY
• AND WHICH AS THE SECONDARY
• ENTIRE HISTORY OF WAVEFORM MUST BE CONSIDERED

• HIGHER FREQUENCY IS AN INTEGER MULTIPLE OF THE LOWER FREQUENCY...EX: 200HZ AND 400HZ
• DETERMINE THE PHASE RELATIONSHIP BY LOOKING AT THE PHASES OF WAVEFORMS AT THE BEGINNING OF ANY CYCLE OF THE LOWER FREQUENCY WAVEFORM.

• HIGHER FREQUENCY IS NOT AN INTEGER MULTIPLE OF THE LOWER FREQUENCY
• EX: 135HZ AND 600 HZ

• MUST INCLUDE A UNIT OF MEASUREMENT EX: 20M OR 400
• CAN BE CONSTANT OR VARY IN TIME

• INSTANTANEOUS MAGNITUDE
• MAGNITUDE OBSERVED AT ANY GIVEN MOMENT IN TIME

AMPLITUDE IS MAGNITUDE OF A PERIODIC WAVEFORM MAXIMUM OR PEAK

IN SIMPLE HARMONIC MOTION, PEAK TO PEAK MAGNITUDE IS TWICE AS LARGE AS THE WAVEFORM AMPLITUDE.

IF THE WAVEFORM IS NOT SYMMETRICAL, IT MAY HAVE DIFFERENT POSITIVE (+) AND NEGATIVE (-) VALUES, AND THE P2P VALUE IS DIFFERENT BETWEEN BOTH AMPLITUDES.

AVERAGE ANY SIMPLE HARMONIC WAVEFORM WILL ALWAYS BE 0.

TAKE NEGATIVE PART OF CYCLE AND FLIP IT UP.

Aua=2A/PIE

SEE EXAMPLE PAGE 15 ON HAND OUT 8/31/10

• ROOT MEAN SQUARE (RMS) AMPLITUDE (Ams)
• THE CONSTANT MAGNITUDE (ONE VALUE) THAT WOULD PRODUCE THE SAME POWER AS THE ORIGINAL QUANTITY OF THE WAVEFORM (MAGNITUDE THAT VARIES)

Arms=A/√2=Ax0.707

• A MODEL USED TO STUDY PHENOMENA ASSOCIATED WITH SIMPLE HARMONIC MOTION INCLUDING:
• MASS
• STIFFNESS
• AND FRICTION EFFECTS

• AMOUNT OF MATTER
• A MASS WILL VIBRATE BACK AND FORTH IN A SIMPLE HARMONIC MOTION BECAUSE OF INTERACTION
• BETWEEN FORCE OF ELASTICITY AND
• FORCE OF INERTIA

MECHANIC PROPERTIES OF ELASTIC BODY THAT DESCRIBES ITS OPPOSITION TO CHANGE IN DIMENSION ALSO INVERSE OF COMPLIANCE

FORCE OPPOSES RELATIVE MOTION OF A BODY THAT IS IN CONTACT WITH OTHER BODIES

• PENDULUM
• *INITIAL DISPLACEMENT IS DETERMINED BY HOW FAR THE PENDULUM IS PULLED AWAY BY AN EXTERNAL FORCE. EX THE AMOUNT OF FORCE APPLIED TO THE SYSTEM

• MASS AND SPRING
• *INITIAL AMPLITUDE IS DETERMINED BY THE FORCE THAT IS APPLIED TO THE MASS

STATES THE FORCE PRODUCED BY AN ELASTIC OBJECT IS LINEARLY PROPORTIONAL TO IT'S EXTENSION.

IF A SPRING IS EXTENDED, THE FORCE OF ELASTICITY WORKS AGAINST THE EXTENSION.

IF THE SPRING IS COMPRESSED, THE FORCE OF ELASTICITY WORKS AGAINST THE COMPRESSION.

THE FARTHER AWAY THE SPRING IS STRETCHED OR COMPRESSED, THE GREATER THE FORCE OF ELASTICITY.

AS THE OBJECT MOVES CLOSER TO ITS EQUILIBRIUM POSITION, THE EFFECT OF THE FORCE ELASTICITY DECREASE, BUT THE OBJECT MAXIMUM VELOCITY BECAUSE OF THE FORCE OF INTERTIA. OR INCREASES VELOCITY.

WHEN THE SPRING REACHES EQUILIBRIUM THE FORCE OF ELASTICITY IS EQUAL TO ZERO, BUT THE MASS MOVES FURTHER DUE TO THE FORCE OF INERTIA (Fm)

INTERACTION BETWEEN THE FORCES OF ELASTICITY AND INTERTIA DETERMINES THE FREQUENCY OF THE BACK AND FORTH MOVEMENT OF THE VIBRATING SYSTEM (THE RESONANCE FREQUENCY).

• FREE VIBRATION
• DEFINED AS THE BACK AND FORTH VIBRATION OF A SYSTEM ONCE ITS INITIALLY SET INTO MOTION.

• RESONANCE FREQUENCY (Fr)
• DEFINED AS THE FREQUENCY OF FREE VIBRATION.
• SIMPLE VIBRATING SYSTEMS HAVE ONE RESONANCE FREQUENCY.
• COMPLEX VIBRATING SYSTEMS MAY HAVE SEVERAL RESONANCE FREQUENCIES.

• IS DETERMINED BY THE MASS, STIFFNESS AND FRICTION OF THE SYSTEM
• *IS THE FREQUENCY AT WHICH A SYSTEM SET INTO FORCED VIBRATION WILL VIBRATE WITH ITS GREATEST MAGNITUDE

• FORCED VIBRATION
• *VIBRATION IN WHICH A SYSTEM IS FORCED TO VIBRATE BY A CONTINUOUSLY OR PERIODICALLY APPLIED EXTERNAL FORCE.

THE RESONANCE FREQUENCY FOR A MASS AND SPRING SYSTEM DEPENDS ON THE STIFFNESS OF THE SPRING AND THE AMOUNT OF MASS.

LARGE OR LOOSE MASS WILL HAVE LOWER RESONANCE FREQUENCY

SMALLER MASS OR STIFFER WILL HAVE HIGHER RESONANCE FREQUENCY.

*BOTH THE PENDULUM AND THE MASS AND SPRING SYSTEM STOP MOVING BECAUSE OF FRICTION.

*FRICTION RESULTS IN THE TRANSFER OF ENERGY FROM KINETIC ENERFY TO THERMAL ENERGY (HEAT)

• *MASS AND SPRING SYSTEM
• FRICTION IS CAUSED BY THE RUBBING OF PARTS OF THE VIBRATING SYSTEM AGAINST SURROUNDING SURFACES AND AIR PARTICLES.

THE EFFECT OF FRICTION ON A VIBRATING SYSTEM IS CALLED DAMPING, AND THE RESULTING VIBRATION IS CALLED DAMPED VIBRATION.

IF THERE IS NO FRICTION, THE WAVEFORM MAINTAINS THE SAME AMPLITUDE OVERTIME.

• A SYSTEM IS MINIMALLY DAMPED (OR UNDERDAMPED) IF THERE IS VERY LITTLE FRICTION IN THE SYSTEM.
• DAMPING WILL STILL MAINTAIN SAME FREQUENCY.

TEMPORAL ENVELOPE IS A GRADUAL DECREASE.

A SYSTEM IS SAID TO BE HEAVILY DAMPED (OR OVERDAMPED) IF THERE IS A LOT OF FRICTION IN THE SYSTEM.

*HEAVILY DAMPED HAS MORE FRICTION...NO OSCILLATIONS DUE TO TOO MUCH FRICTION.

• A SYSTEM IS SAID TO BE CRITICALLY DAMPED IF THE OBJECT WILL MAKE ONLY ONE VIBRATION AND THEN RETURN TO IT'S NATURAL POSITION AS FAST AS POSSIBLE.
• CRITICALLY DAMPED CUTS OFF THE VIBRATION EVEN FASTER AND THEN DOESNT DO ANYTHING ELSE.

• RISE TIME (GROWTH TIME OR ATTACK TIME)
• TIME NEEDED FOR A WAVEFORM TO CHANGE FROM 10% TO 90% OF ITS PEAK VALUE (FULL AMPLITUDE)

STEADY-STATE TIME (SUSTAIN TIME)

FALL TIME (DECAY TIME, ROLL-OFF TIME)

TIME NEEDED FOR A WAVEFORM TO CHANGE FROM 90% TO 10% OF ITS PEAK VALUE (FULL AMPLITUDE)

OCCURS IF A SYSTEM IS NOT ALLOWED TO VIBRATE FREELY BUT INSTEAD IS FORCED TO VIBRATE BY A CONTINUOUS AND PERIODIC DRIVING FORCE.

DRIVING FREQUENCY-FREQUENCY OF THE EXTERNAL DRIVING FORCE

IN A FORCED MODE OF VIBRATION, THE SYSTEM WILL VIBRATE BACK AND FORTH AT THE FREQUENCY OF THE DRIVING FORCE.

START SOMETHING IN VIBRATION AND KEEP FORCING IT TO VIBRATE IN ANOTHER FREQUENCY "DRIVING FORCE"

• THE MAGNITUDE OF VIBRATION DEPENDS ON THE:
• *MAGNITUDE OF THE APPLIED FORCE
• *FREQUENCY OF THE DRIVING FORCE
• *RESONANCE FREQUENCY OF THE SYSTEM BEING FORCED TO VIBRATE
• *FRICTION IN THE VIBRATING SYSTEM

***IF A SYSTEM IS FORCED TO VIBRATE CLOSE TO OR AT ITS RESONANCE FREQUENCY, THE SYSTEM WILL VIBRATE WITH A GREATER MAGNITUDE THAN IF THE SAME SYSTEM IS FORCED TO VIBRATE AT A FREQUENCY THAT IS MUCH LOWER OR MUCH HIGHER THAN THE RESONANCE FREQUENCY.