The nature of waves:
  • A wave is a traveling disturbance
  • A wave carries energy from place to place
Mechanical Waves
  • require a medium to propogate
Non- Mechanical Waves
  • do no require a medium to propogate
Longitudinal Waves
  • particle motion is in the same direction as the waves motion (direction of propogation)
Transverse Waves
  • particle motion is perpendicular to the direction of the wave propogated
external image wave.jpg

-rope, tightly coiled slinky
-"The Wave"


Wavelength= meters
Speed of light= 3.08*10^8 meters per second
Period= seconds
Frequency= 1/seconds= Hz
Amplitude= meters


Properties of the Speed of Sound
  • The speed of sound is faster in a solid than in a liquid and faster in a liquid than in a gas. Solid > Liquid > Gas
  • The smaller/lighter the mass of the molecule in gases the faster the speed of sound.
  • The higher the temperature the faster the speed of sound because the molecules travel faster when it is hotter.

Speed of a Wave
  • determined by the medium traveled through
  • V=wavelength/period= λf
  • Speed of wave on string=√(T/u) where T= tension of a string and u=linear mass density
  • An object will vibrate at its natural frequency

Principle of Super Position

  • positive amplitude= molecules more compressed, dense
  • speed of sound wave in air is the same for all notes and frequencies, only the wavelength changes

Two Speakers Producing the Same Sound
  • Δd=d2-d1=path difference between the two sound wave
  • Constructive Interference in phase: Δd=nλ
  • Destructive Interference in phase: Δd=(n+1/2)λ
  • Constructive Interference: When the troughs and peaks of a wave line up to produce an amplified sound
  • Destructive Interference: When the trough of a wave meets with the peak of another wave, sounds cancels out
  • Out of phase: half a cycle off, equations for construcive interference and destructive interference are the same except switched
    This is a picture showing an out of phase wave. The red wave is exactly 180 degrees out of phase with the blue wave.

    A good video depicting the motions of a sound wave and other important qualities of a sound wave is the following:

Wave Problems

1. A sound wave has a frequency of 262 Hz. What is the time between successive wave crests?
Period = 1/ Frequency
Period = 1 / 262 Hz
Period = .0038s

2. A sound wave produced by a clock chime 515 m away is heard 1.50 s later. The frequency of the sound
is 436 Hz.
(a) What is the speed of sound in air?
(b) What is the period of the sound wave?
(c) What is its wavelength?

(a) Velocity = delta distance / delta time
Velocity = 515m / 1.50s = 343.3 m/s

(b) Period = 1 / Frequency
Period = 1 / 436 Hz
Period = .00229s

(c) Velocity = Wavelength * Frequency
Velocity / Frequency = Wavelength
343.3 m/s / 436 Hz = .7874 m
Suppose that the two speakers in the figure are separated by 2.50 m and are vibrating exactly out of phase at a frequency of 429 Hz. The speed of sound is 343 m/s. Does the observer at C observe constructive or destructive interfernce when his distance from speaker B is

external image ch17p_6.gif
  1. The Δd would can be find by finding the difference between the AC and BC.
  2. BC and AB are given and it can be seen in the pictuce that angle ABC is 90 degrees.
  3. AC can be found using the pythagorean theorem.
  4. AB^2 + BC^2 = AC^2
  5. AC = 4
  6. Δd = 4m - 2.4m = 1.6m
  7. Now we need to find the wavelength
  8. Velocity = Wavelength * Frequency
  9. Wavelength = Velocity / Frequency = .800m
  10. (Δd/λ) - .5 will determine whether or not the there is constructive or destructive interference.
  11. (16m/.800m) - .5 = 1.5 There is destructive interference.

Website with good description and animation of constructive and dustructive interference

Interesting Videos, pictures, and links

World War One acoustic mirror, Kilnsea, East Yorkshire, UK. Concrete mirrors like these were constructed before the invention of radar to detect the sound of approaching enemy aircraft.
World War One acoustic mirror, Kilnsea, East Yorkshire, UK. Concrete mirrors like these were constructed before the invention of radar to detect the sound of approaching enemy aircraft.

Image of the Acoustic Mirror