Review: Key characteristics of waves All of these terms are required for the Regents Amplitude: The height of the wave from node to antinode (transverse waves), or the pressure in a compressive wave. Measured in units describing the wave Wavelength: The distance traversed by a full cycle of the wave Node: The “zero point” of the wave Antinode: The extreme point of the wave (max or min amplitude) Period: The time between successive waves Frequency: The rate of occurrence of the wave (in Hertz or cycles / second) The frequency f = 1/T where T is the period. Period (if axis is time)

Sound Waves

How is Sound Transmitted? Sound is created by the cyclical collisions of atoms and molecules such that it is transmitted through the bulk matter. www.library.thinkquest.org

Speed of Sound Speed of sound depends on the medium through which it travels. kT m Where: k = Boltzman’s constant (1.38 x 10-23 J/K)  = Cp/Cv (~5/3 for ideal monotonic gases) T = Temperature (K) m = Average mass of air (~28.9 amu) Air Water Steel Speed (m/s) 343 1482 5960 vrms =

Speed of Sound What happens if the speed of sound changes but the frequency (vibration source) remains the same? MythBusters!

Sound Wave Characteristics Condensation or Compression: Region of the wave where air pressure is slightly higher. Rarefaction: Region of the air wave where the pressure is slightly lower. Pure Tone: A sound wave with a single frequency. Pitch: An objective property of sound associated with frequency. Pitch High frequency = high pitch. Low frequency = low pitch. Loudness: The attribute of sound that is associated with the amplitude of the wave. Beat: When two sound waves overlap with a slightly different frequency, the beat frequency is heard as the difference between them Beats

Standing Waves in Musical Instruments Resonance: Stringed instruments, such as the guitar, piano or violin, and horn and wind instruments such as the trumpet, oboe, flute and clarinet all form standing waves when a note is being played. The standing waves are of either the type that are found on a string, or in an air column (open or closed). These standing waves all occur at natural frequencies, also known as resonant frequencies, associated with the instrument.

Standing waves Two similar periodic waves traveling in opposite directions form a standing wave.

Standing Wave Characteristics While a standing wave does not travel itself, it is comprised of two waves traveling in opposite directions. Harmonic: The series of frequencies where standing waves recur (1f, 2f, 3f,…). Where the first frequency is called the first harmonic (1f), the second frequency is called the second harmonic (2f), and so on. The first harmonic = the first fundamental frequency (n = 1). Overtones: The harmonic frequency + 1.

Harmonics and Overtones of Standing Waves www.cnx.rice.edu

Standing Wave Characteristics (cont.) The time for one wave to travel to the barrier and back is: T = 2L/v For a string fixed at both ends with n antinodes: fn = n(v/2L) n = 1, 2, 3, … Each fn represents a natural or resonant frequency of the string. This relationship can be rewritten for  as follows.  = 2L/n www.electron4.phys.utk.edu www.cord.edu

Longitudinal Standing Waves Wind instruments, such as the flute, oboe, clarinet, trumpet, etc. develop longitudinal standing waves. They are a column of air. May be open at one or both ends. Wave will reflect back regardless as to whether or not it is open or close ended.

Longitudinal Standing Waves – Open Tube In an open tube instrument like the flute, the harmonics follow the following relationship: fn = n(v/2L) n = 1, 2, 3, … www.cnx.rice.edu Longitudinal Standing Wave Applet

Longitudinal Standing Waves –Tube Closed on One End In a closed tube instrument like the clarinet or oboe, the harmonics follow the following relationship: fn = n(v/4L) n = 1, 3, 5, … www.cnx.rice.edu

How does a string make music? What does a string look like when vibrating? How do I measure Amplitude Wavelength Frequency Period For each of these? Pause for responses 15

V = nf/2L L = l/2

Key Ideas Sound waves are generated by a vibrating object such as the string on a violin, your vocal chords or the diaphragm of a loudspeaker. Sound waves can be transmitted through gases, liquids and solids. If there is no medium, there is no sound. Sound is generated by the cyclical collisions of atoms and molecules. Condensation and rarefaction denote portions of the wave that are of slightly higher and lower pressure, respectively.

Key Ideas Sound waves travel at different speeds in different mediums. They speed up when going from air to a liquid to a solid. Pure tone is sound of a single frequency. Pitch and loudness are characteristics of sound that represent its frequency and amplitude, respectively. When two sound waves overlap slightly due to mildly different frequencies, they generate a beat. Harmonics occur at multiples of the natural frequency.

Waves: Doppler Shift Mr. Davis

Doppler Shift The change in sound frequency due to the relative motion of either the source or the detector. www.physicsclassroom.com High Pitched Sound Low Pitched Sound Doppler Video

The Doppler Effect http://www.youtube.com/watch?v=19_727LxYDw http://www.youtube.com/watch?v=imoxDcn2Sgo http://www.youtube.com/watch?v=a3RfULw7aAY This and the following slides are tools from the Doppler Effect tutorial.

Doppler This demo shows the Doppler effect in action Doppler (Falstad: Needs to be set to correct option) Doppler Simulation

Waves: Superpositioning Mr. Davis

What happens when two waves collide? They pass through each other without changing and keep on going. (Have you ever crossed the beams of two flashlights to see what would happen?) Does anyone recognize a common application for the second example? (AM rdio) 26

When two waves pass, at any given instant add the amplitudes – that sum gives you the amplitude of the combined wave. Given the right (infinite) number of sine waves, we can add them up to make any waveform we want!

Adding sine waves to make a square wave: One wave

Adding sine wives to make a square wave: Two waves

Adding sine wives to make a square wave: Wave One + Wave 2

Adding sine wives to make a square wave: Waves One through Wave Eight

Adding sine wives to make a sawtooth wave: Waves One through Wave Eight and Waves One through Wave Fifteen

Superposition on a piano Hear the bells? http://www.rtcutler.com/Audio/MilhaudBells.mp3 Physics today, July 2015, p. 9, Letter from Roger Cutler, “A final note on bell-like tones.

Surface Waves

Surface Wave A wave that has characteristics of both transverse and longitudinal waves (Ocean Waves). Surface Wave Applet

Surface Waves Thus far, you have seen the profile view of waves. How do these waves look from above? Direction of propagation Wavefronts l = Wavelength

Reflection of Surface Waves The law of reflection states that the angle of incidence is equal to the angle of reflection. (Video) Note the constructive interference. Wave Crest r i Reflected Ray Normal i = r Incident Ray

Standing Wave T = 2L/v fn = n(v/2L) n = 1, 2, 3, … The time for one wave to travel to the barrier and back is: T = 2L/v When the reflected wave is the same frequency as a natural frequency of the system, resonance occurs (sometimes extreme) fn = n(v/2L) n = 1, 2, 3, … Tacoma Narrows Bridge www.electron4.phys.utk.edu www.cord.edu

Refraction of Surface Waves If the direction of the wave changes, then the wave is said to have refracted. Refraction. (Falstad) (PHET) (Video) (Fendt – broken: 2017)

Refraction of Surface Waves When surface waves move from deep water to shallower water: The wavelength decreases. The amplitude increases. The speed decreases. Why? Because of interactions with the bottom. Note: The frequency does not change!

Interference As per the principle of linear superposition: Crests will combine with crests and troughs will combine with troughs in a constructive manner. Where a crest meets a trough, interference will be totally destructive. Constructive Interference Destructive Interference (Video – Beach) (Video – Ship)

Diffraction When a wave front is incident on a barrier with an opening, the wave will spread out after crossing the barrier. This process is called diffraction. As the slit becomes narrower, the amount of diffraction will increase. As the wavelength increases, the amount of diffraction increases. Wavelength, frequency, and hence velocity, do not change. Diffraction (PHET) (Falstad)

Key Ideas Surface waves have characteristics of both transverse and longitudinal waves. Waves transfer energy without transferring matter. Waves can interfere with one another resulting in constructive or destructive interference. The law of reflection states that angle of incident wave equals the angle of the reflected wave. Diffraction is the spreading out of a wave when it encounters a barrier.

Law of Reflection The angle of incidence with respect to the normal is equal to the angle of reflection.