Vibrations & Sound

• PERIOD

  • time taken for one complete cycle (one wavelength)
  • variable: T
  • unit: S
• FREQUENCY

  • number of cycles per second
  • variable: f
  • unit: hertz (hz)
• period & frequency are inverses of each other

  • t = 1/f
  • f = 1/t
• crest: high point of wave
• trough: low point of wave
• SOUND

  type of energy made by vibrations (when an object vibrates, it causes movement in surrounding air molecules)
• amplitude: distance from midpoint to crest

  • variable: A
  • unit: meters
• wavelength: distance from crest to crest

  • variable: lambda
  • unit: meters
• TYPES OF WAVES

  • TRANSVERSE: motion of medium is perpendicular to direction the wave travels
  • LONGITUDINAL: motion of medium is in the same direction the wave travels
• PITCH

  our perceived frequency of a sound (higher pitched sound, higher frequency)
• young people can hear pitches with frequencies ranging from 20 - 20,000 hz

  • INFRASONIC: sound waves with frequencies below 20 hz
  • ULTRASONIC: sound waves with frequencies above 20,000 hz
• sound travels in the form of longitudinal waves

  • a pulse vibrates through the air as a series of compressions and rarefactions
  • when molecules compress, they leave areas of low pressure behind them
  • other molecules will move into these regions
• SOUND TRANSMISSION

  • speed of sound is different in different materials
  • faster in solids than liquids, gases
  • faster in hot weather than cold
  • sound cannot travel in a vacuum
• WAVE SPEED depends on the medium

  • wavelength x frequency (c = lambda f)
• LOUDNESS

  • intensity of a sound relates to the amplitude
  • greater amplitude, greater loudness
  • measured with oscilloscope
  • LOUDNESS is how our brain senses the sound (volume)
• SOUND INTENSITY

  I = power/area (P/ pi r squared)

  • measured in watts per square meter
  • sound intensity LEVEL is measured in Decibels (dB)
  • IMPORTANT NOTE: doubling the sound intensity increases the sound intensity level by 3dB
• • CONSTRUCTIVE INTERFERENCE: crest of one wave overlaps crest of another (increased amplitude)
  • DESTRUCTIVE INTERFERENCE: crest of one wave overlaps trough of another (cancellation of amplitude)
• STANDING WAVES

  • created when a wave reflects on itself
  • NODES: positions on a standing wave which remain stationary
  • ANTINODES: positions on a standing wave with the largest amplitudes
• INTERFERENCE & BEATS

  • a receiver may hear two sound waves at the same time:
  • IN PHASE: compressions and rarefactions overlap each other
  • OUT OF PHASE: compressions and rarefactions of each wave are offset
• BEATS: the periodic variation in the loudness of a sound (produced from two sounds of slightly different frequencies)
• FUNDAMENTAL FREQUENCY: frequency of the lowest harmonic of a wave (first harmonic)
• fundamental frequency of a string is related to its length

  • f is proportional to 1/length
• FACTORS THAT DETERMINE THE FUNDAMENTAL FREQUENCY OF A VIBRATING STRING?

  tension, length, mass per unit length

  • higher tension, higher fundamental frequency (f proportional to root t)
  • greater length, lower fundamental frequency (f proportional to 1/length)
  • greater mass per unit length, lower fundamental frequency (f proportional to 1/root mu)
• GOOD SOUND QUALITY

  has little to no overtones. more overtones, less quality. also depends on strength of the overtones.
• FORCED VIBRATIONS

  • sound will be more intense if additional material is made to vibrate (guitar would not be audible if the sound wasn't transmitted through its wooden body, waves along the string cause vibrations in the wood)
• NATURAL FREQUENCY

  • frequency at which the smallest amount of energy is required to produce forced vibrations
  • depends on elasticity and shape
• RESONANCE

  when the frequency of a forced vibration matches the object's natural frequency, it dramatically increases the amplitude of the sound wave
• DOPPLER EFFECT

  the apparent change in frequency due to the motion of the source or the observer

  • applications: ambulance, speed cameras
• DOPPLER EFFECT FORMULA

  • f' = fc/c+-u
  • f' (apparent frequency)
  • f (actual frequency)
  • c (velocity of wave)
  • + (wave moving away from observer)
  • -- (wave moving towards observer)
  • u (velocity of observer/source)
• TO DEMONSTRATE DOPPLER EFFECT

  rope, tennis ball, buzzer
• TO DEMONSTRATE RESONANCE

  tuning forks of the same frequency, place one on hollow box, strike the other and hold it against the box to hear the sound, remove this and the other fork will audibly vibrate