Vibrations and sound

• Natural frequency

  The frequency at which an object will vibrate if it is free to do so
• Factors determining natural frequency of a stretched string

  • Frequency is inversely proportional to the length of the string
  • Frequency is directly proportional to the square root of the tension in the string
  • Frequency is inversely proportional to the square root of the mass per unit length of the string
• Frequency

  Inversely proportional to the length of the string
• Frequency

  Directly proportional to the square root of the tension in the string
• Frequency

  Inversely proportional to the square root of the mass per unit length of the string
• Resonance

  The transfer of energy so that a body vibrates at its natural frequency
• Unit of sound intensity

  Power per unit area
• The threshold of hearing is the smallest sound intensity detectable by the average human ear at a frequency of 100 hertz to the power of 13
• Doubling the sound intensity

  Increases the sound intensity level by 3 decibels
• Harmonics

  Integer multiples of the fundamental frequency
• Fundamental frequency


  The basic frequency
• Overtones

  Frequencies which are multiples of a given frequency
• Characteristics of notes

  • Loudness
  • Pitch
  • Quality
• Loudness

  Depends upon the amplitude of the sound wave
• Pitch

  Depends upon the frequency of the sound wave
• The Qualityof a note

  Depends upon the number of overtones present in the note and the relative strengths of those different overtones.
• Most sounds vibrate at a fundamental frequency plus overtones
• frequency of a stretched string

  The formula