Chapter 13: Sound

13-1: Sound Waves

The Production of Sound Waves
  • Compression- The region of a longitudinal wave in which the density and pressure are greater than normal
  • Rarefaction- The region of a longitudinal wave in which the density and pressure are less than normal
  • Sound waves are longitudinal

Characteristics of Sound Waves
  • Sound waves that the average human ear can hear are called audible sound waves.
  • They have frequencies between 20 and 20 000 Hz.
  • Sound waves with frequenices less than 20 Hz are called infrasonic waves.
  • Those above 20 000 Hz are called ultrasonic waves.
  • Frequency determines pitch.
  • Pitch- The perceived highness or low-ness of a sound, depending on the frequency of the sound waves.
  • Ultrasonic waves can produce images.
  • Speed of sound depends on the medium.
  • Sound waves propagate in three dimensions.
  • The circles that represent the centers of compression are called wave fronts.
  • The radial lines perpendicular to the wave fronts are called rays.
  • Any small portion of a spherical wave that is far from the source can be considered a plane wave.

The Doppler Effect
  • Relative motion creates a change in frequency.
  • Doppler effect- A frequency shift that is the result of relative motion between the source of waves and an observer.
  • The Doppler effect occurs whenever there is relative motion between the source of waves and an observer.

13-2: Sound Intensity and Resonance

Sound Intensity
  • Intensity is the rate of energy flow through a given area.
  • Intensity- The rate at which energy flows through a unit area perpendicular to the direction of wave motion.
  • Because power, P, is deined as the rate of energy transfer, intensity can also be described in terms of power.
  • The SI unit for power is the watt, thus intensity has units of watts per square meter (W/m²).
  • Internsity of a spherical wave.
    • Intensity= (P/4πr²)
  • Intensity and frequency determine which sounds are audible.
  • Threshold of hearing- The softest sounds that can be heard by the average human ear occur at a frequency of about 1000 Hz and an intensity of 1.0 X 10¯¹² W/m².
  • Threshold of pain- The loudest sounds that the human ear can tolerate have an intensity of about 1.0 W/m².
  • Relative intensity is measure in decibles.
  • Decibel level- Relative intensity, determined by relating the intensity of a sound wave to the intensity at the threshold of hearing.

Forced Vibrations and Resonance

  • Vibration at the natural frequency produces resonance.
  • Resonance- A condition that exists when the frequency of a force applied to a system matches the natural frequency of vibration of the system.
  • The human ear transmits vibrations that cause nerve impluses.

13:3 Harmonic

Standing Waves On a Vibrating String
  • Fundamental frequency- The lowest frequency of vibration of a standing wave.
  • Harmonics are integral multiples of the fundamental frequency.
  • Harmonic series- A series of frequencies that includes the fundamental frequency and integral multiples of the fundamental frequency.
  • Harmonic series of standing waves on a vibrating string:
    • Fn=n(V/2L) n= 1,2,3,...
Standing waves in an air column
  • If both ends of a pipe are open, all harmonics are present
  • Harmonic series of a pipe open at both ends:
    • Fn=n(V/2L) n= 1,2,3,...
  • If one end of a pipe is closed, only odd harmonics are present
  • Harmonic series of a pipe closed at one end:
    • Fn=n(V/4L) n= 1,3,5,...
  • Harmonics account for sound quality, or timbre.
  • Timbre- The quality of a steady musical sound that is the result of a mixture of harmonics present at different intensities.
  • Notes that each consist of repeating patterns are said to be periodic.
  • Fundamental frequency determines pitch.
  • The frequency of the thirteenth note is exactly twice that of the first note, and togeather the 13 notes constitute an octave.

  • When two waves of slightly different frequencies interfere, the interference pattern varies in such way that a listener hears an alternation between loudness and softness.
  • Beat- Interference of waves of slightly different frequencies traveling in the same direction, perceived as a variation in loudness.
  • Sound waves at slightly different frequencies produce beats.
  • When the two waves are exactly opposite one another, they are said to be out of phase.
  • The number of beats per second corresponds to the difference between frequencies.
  • The expansion of the universe.
  • The eruption of the universe is often referred to as the big bang.
  • Experimental verification.

Practice Problems:

1) Calculate the intensity of the sound waves from an electric guitar's amplifier at a distance of 5.0m when its power output is equal to each of the following values:
a. 0.25 W
b. 0.50 W
c. 2.0 W
2) If the intensity of a person's voice is 4.6 X 10^ -7 W/m² at a distance of 2.0 m, how much sound power deos that person generate?

3) The power output of a tuba is 0.35 W. At what distance is the sound intensity of the tube 1.2 X 10^ -3 W/m²?

4) What is the fundamental frequency of a 0.20 m long organ pipe that is closed at one end, when the speed of sound in the pipe is 352 m/s?

5) What is the fundamental frequency of a guitar string when the speed of waves on the string is 115 m/s and the effective string lengths are as follows:
a. 70.0 cm
b. 50.0 cm
c. 40.0 cm

1. a. 8.0 X 10^ -4 W/m², b. 1.6 X 10^ -3 W/m², c. 6.4 X 10^ -3 W/m²
2. 2.3 X 10^ -5 W
3. 4.8 m
4. 440 Hz
5. a. 82.1 Hz, b. 115 Hz, c. 144 Hz

Holt, Rinehart and Holt Physics. New York: Holt, Rinehart & Winston, 2001.