Waves and Sound

Wave A disturbance or oscillation that travels through space and matter, accompanied by a transfer of energy. Big Idea 6: Waves can transfer energy and momentum from one location to another without the permanent transfer of mass and serve as a mathematical model for the description of other phenomena.

Parts of the wave

Definitions Essential Knowledge 6.B.1: For a periodic wave, the period is the repeat time of the wave. The frequency is the number of repetitions of the wave per unit time. Essential Knowledge 6.B.4: For a periodic wave, wavelength is the ratio of speed over frequency. Essential Knowledge 6.A.3: The amplitude is the maximum displacement of a wave from its equilibrium value.

Frequency and speed of a wave 𝑓= 1 𝑇 𝑣= 𝑓 for electromagnetic waves, v = c = 3.0 x 108 m/s

Wave in a string The speed of a wave traveling on a stretched string of mass per unit length  and under tension F is: 𝑣= 𝐹 

Types of waves Essential Knowledge 6.A.1: Waves can propagate via different oscillation modes such as transverse and longitudinal. a. Mechanical waves can be either transverse or longitudinal. Examples should include waves on a stretched string and sound waves. b. Electromagnetic waves are transverse waves.

Transverse wave A transverse wave is one in which the disturbance is perpendicular to the direction of travel of the wave. Examples: Light wave, waves on a guitar string.

Longitudinal wave Longitudinal wave is one in which the disturbance is parallel to the line of travel of the wave. Example: Sound wave in air is a longitudinal wave.

Superposition principle When two waves interact, the resulting wave function is the sum of the two individual wave functions. This phenomena is generally described as interference. When crest and crest or trough and trough meet, they add up creating a bigger wave. This is constructive interference. When a crest and a trough meet, they cancel each other. This destructive interference.

Superposition Essential Knowledge 6.C.1: When two waves cross, they travel through each other; they do not bounce off each other. Where the waves overlap, the resulting displacement can be determined by adding the displacements of the two waves. This is called superposition.

Constructive Interference They will ADD together to produce a greater amplitude.

Destructive Interference This time when they add together they will produce a smaller amplitude.

Standing Wave Features: Standing Waves …a wave in which the amplitude at a given location does not vary with time. Standing Wave Features: Amplitude is zero at fixed ends Nodes (other places with zero amplitude) Anti-nodes (places with maximum amplitude)

Standing Wave: Both Ends Fixed

Standing Wave: One End Fixed, One End Free

vsound = 331.5 m/s + (TC)(0.6 m/s∙C) Longitudinal Needs a medium Can not be polarized. The speed of sound in air is affected by the air temperature as given in the following formula: vsound = 331.5 m/s + (TC)(0.6 m/s∙C)

Doppler effect The change in frequency heard by an observer whenever there is relative motion between the source and the observer. Essential Knowledge 6.B.5: The observed frequency of a wave depends on the relative motion of source and observer.

Doppler effect

Source in Motion

Source moving at speed of sound

Source moving faster than sound

Resonance Resonance is the tendency of a system to oscillate with greater amplitude at some frequencies than at others. Happens in an air column whenever a standing wave is formed.

Closed-pipe Resonator open at one end and closed at the other resonance will occur whenever there is a node at the closed end and an antinode at the open end

Closed-pipe Resonator 𝑳 𝒏 = (𝟐𝒏 − 𝟏)  𝟒 Note: resonant lengths of a closed-pipe resonator are odd multiples of one-quarter wavelength

Open-pipe Resonator open-pipe air column is open at both ends resonance will occur whenever there is an antinode at both open ends

Open-pipe Resonator 𝑳 𝒏 = 𝒏 𝟐 Note: resonant lengths of an open-pipe resonator are multiples of one-half wavelength

Beat Oscillation of wave amplitude that occurs as a result of the superposition of two sound waves having nearly identical frequencies 𝑓 𝑏𝑒𝑎𝑡 = 𝑓 𝐴 − 𝑓 𝐵