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Physics sound and waves notes, Study notes of Physics

Physics

Sound and waves notes to study

Typology: Study notes

2021/2022

Uploaded on 05/21/2023

dhruv-padhiyar
dhruv-padhiyar 🇨🇦

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Dhruv sound and waves notes
Sinusoidal waves: The individual particles oscillate back & forth with a displacement that follows
a sinusoidal pattern In any waveform, energy is delivered in the direction of wave travel
Transverse waves: The direction of particle oscillation is PERPENDICULAR to the propagation
(movement) of the wave. The particles are oscillating perpendicular to the direction of energy
transfer
Longitudanal waves: The particles of the wave oscillate PARALLEL to the direction of
propagation.The wave particles are oscillating in the direction of energy transfer
example: sound waves. Can be created by a person moving a piston back & forth causes air
molecules to oscillate through cycles of compression & rarefaction (decompression) along the
direction of motion of the wave
Description of waves:Crest: a maximum of the wave
Trough: a minimum of the wave
Wavelength : the distance from 1 crest to the next
Frequency (f): the number of wavelengths passing a fixed point per second
Measured in hertz (Hz) or cycles per second (cps)
Propagation speed (v):v=fλ
Period (T): the number of seconds per cycle; inverse of frequency
Angular frequencyMeasured in radians per second
Often used in consideration of simple harmonic motion in springs & pendula
Equilibrium position: a central point which waves oscillate about
Displacement (x): describes how far a particular point on the wave is from the eqbm
Position. Expressed as a vector quantity Amplitude the maximum magnitude of displacement in
a wave
Phase difference: calculated for waves to determine how “in step” or “out of step” the waves are
Consider 2 waves that have the same frequency, wavelength, and amplitude & that pass
through the same space at the same time.
Principle of superposition: When waves interact with each other, the displacement of the
resultant wave at any point is thesum of the displacements of the 2 interacting waves
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Dhruv sound and waves notes Sinusoidal waves: The individual particles oscillate back & forth with a displacement that follows a sinusoidal pattern In any waveform, energy is delivered in the direction of wave travel Transverse waves: The direction of particle oscillation is PERPENDICULAR to the propagation (movement) of the wave. The particles are oscillating perpendicular to the direction of energy transfer Longitudanal waves: The particles of the wave oscillate PARALLEL to the direction of propagation.The wave particles are oscillating in the direction of energy transfer example: sound waves. Can be created by a person moving a piston back & forth causes air molecules to oscillate through cycles of compression & rarefaction (decompression) along the direction of motion of the wave Description of waves:Crest: a maximum of the wave Trough: a minimum of the wave Wavelength : the distance from 1 crest to the next Frequency (f): the number of wavelengths passing a fixed point per second Measured in hertz (Hz) or cycles per second (cps) Propagation speed (v):v=fλ Period (T): the number of seconds per cycle; inverse of frequency Angular frequencyMeasured in radians per second Often used in consideration of simple harmonic motion in springs & pendula Equilibrium position: a central point which waves oscillate about Displacement (x): describes how far a particular point on the wave is from the eqbm Position. Expressed as a vector quantity Amplitude the maximum magnitude of displacement in a wave Phase difference: calculated for waves to determine how “in step” or “out of step” the waves are Consider 2 waves that have the same frequency, wavelength, and amplitude & that pass through the same space at the same time. Principle of superposition: When waves interact with each other, the displacement of the resultant wave at any point is thesum of the displacements of the 2 interacting waves

Waves perfectly IN phase constructive interference.The displacements always add together The amplitude of the resultant is equal to the sum of the amplitudes of the 2 waves Waves perfectly OUT OF phase destructive interference The displacements always counteract each other. The amplitude of the resultant wave is the difference b/w the amplitudes of the interacting waves If 2 equal waves are exactly 180 out of phase, the resultant wave has zero Amplitude. Waves aren’t perfectly in phase or out of phase with each other partially constructive or partially destructive interference can occur 2 waves that are nearly in phase will mostly add together. Displacement of the resultant is simply the sum of the displacements of the 2 waves The waves don’t perfectly add together bc they’re not quite the same the amplitude of the resultant wave isn’t quite the sum of the 2 waves’ amplitudes Travelling wave: a moving wave If a string is fixed at 1 end and moved up & down, a wave will form & travel (or propagate) toward the fixed end. When the wave reaches the fixed boundary, it’s reflected & inverted oIf the free end of the string is continuously moved up & down, there will be 2 waves:

  1. Original wave moving down the string toward the fixed end
  2. Reflected wave moving away from the fixed end These waves will interfere with each other Standing wave : the only apparent movement of the string is fluctuation of amplitude at fixed points along the length of the string. If both ends of the string are fixed & traveling waves are excited in the string Certain wave frequencies will cause interference b/w the traveling wave & its reflected wave such that they form a waveform that appears to be stationary. Nodes: Points in the wave that remain at rest. Timbre: The quality of the sound Forced oscillation: a system driven at a frequency equal to the frequency of the force as a result of force being applied to the system.

Attenuation: A decrease in amplitude of a wave caused by an applied or nonconservative force Sound isn’t transmitted undiminished Even after the decrease in intensity associated with distance, real world measurements of sound will be lower than those expected from calculations Result of damping. Oscillations are a form of repeated linear motion sound is subject to the same nonconservative forces as any other system (incl. friction, air resistance, and viscous drag). The presence of a nonconservative force causes the system to decrease in amplitude during each oscillation. Amplitude, intensity, and sound level (loudness) are related there’s a corresponding gradual loss of sound. Damping doesn’t have an effect on the frequency of the wave – the pitch won't change. Damping + reflection explains why it’s more difficult to hear in a confined or cluttered space than in an empty room. Friction from the surfaces of the objects in the room decreases the sound waves amplitudes. Over small distances, attenuation is usually negligible. Standing waves: produced by the constructive and destructive interference of a traveling wave and its reflecting wave. will form whenever 2 waves of the same frequency traveling in opposite directions interfere with one another as they travel through the same medium. Appear to be standing still (not propagating) the interference of the wave & its reflected wave produce a resultant that fluctuates only in amplitude. As the waves move in opposite directions, they interfere to produce a new wave pattern characterized by alternating points of maximum displacement (amplitude) & points of no displacement. Strings: Consider string (i.e., a guitar or violin string, piano wire) fixed rigidly at both ends String is secured at both ends & is immobile at these points they’re considered Nodes. A standing wave is set up such that there’s 1 antinode b/w the 2 nodes at the ends the length of the string corresponds to one-half the wavelength of this standing wave. On a sine wave, the distance from 1 node to the next node is one-half of a wavelength 2 antinodes b/w the ends must be a 3rd node located b/w the antinodes. The length of the string corresponds to the wavelength of this standing wave The distance on a sine wave from a node to the 2nd consecutive node is exactly 1 wavelength Pattern suggests that the length L of a string must be equal to some multiple of half-wavelengths. Relationship b/w wavelength of a standing wave & the length of a string that supports it. Harmonic (n): corresponds to the # of half-wavelengths supported by the String. A positive nonzero integer. The possible frequencies: Fundamental frequency (1st harmonic): the lowest frequency (longest wavelength) of a standing wave that can be supported in a given length of string 1st overtone (2nd harmonic): the frequency of the standing wave given by n =2 This standing wave has one-half the wavelength & twice the frequency of the 1st harmonic 2nd overtone (3rd harmonic): the frequency of the standing wave given by n =3 Harmonic series: formed from all the possible frequencies that the string can Support For strings attached at both ends, the number of antinodes present will tell you which harmonic it is.

Open pipes: Pipes that are open at both ends Has antinodes at both ends If a standing wave is set up such that there’s only 1 node b/w the 2 antinodes at the ends, the length of the pipe corresponds to one-half the wavelength of this standing wave 2nd harmonic (1st overtone) has a wavelength equal to the length of the pipe 3rd harmonic (2nd overtone) has a wavelength equal to two-thirds the length of the pipe An open pipe can contain any multiple of half-wavelengths. The number of half-wavelengths corresponds to the harmonic of the wave. Relationship b/w wavelength of a standing wave & the length of an open pipe that supports it: The possible frequencies of the harmonic series: For open pipes, the # of nodes present will tell you which harmonic it is Conventional way of diagramming standing waves is to represent sound waves as transverse, rather than longitudinal, waves. Closed pipes: Pipes that are closed at 1 end (and open at the other) The closed end will correspond to a node. The open end will correspond to an antinode In a sinusoidal wave, the distance from a node to the following antinode is ¼ of a wavelength Harmonic in a closed pipe = the # of quarter-wavelengths supported by the pipe. Closed end must always have a node & open end must always have an antinode there can only be odd harmonics. An even # of quarter-wavelengths would be an integer # of half-wavelengths (would necessarily have either 2 nodes or 2 antinodes at the ends). 1st harmonic: only the node at the closed end & the antinode at the open end; wavelength is 4 the length of the closed pipe. 3rd harmonic (1st overtone): wavelength is four-thirds the length of the closed pipe. 5th harmonic (2nd overtone): wavelength is four-fifths the length of the closed pipe. Relationship b/w wavelength of a standing wave & the length of the closed pipe supporting it:n can only be odd integers. Frequency: Can’t simply count the # of nodes or antinodes to determine the harmonic of the wave in closed pipes. Count the number of quarter-wavelengths contained in the pipe to determine the harmonic Ultrasound: Ultrasound machine consists of a transmitter that generates a pressure gradient, which also functions as a receiver that processes the reflected sound. The transmitter (sender) generates a wave, which reflects off of an object & returns to the transmitter (which also functions as a receiver). The speed of the wave & travel time is unknown the machine can generate a graphical representation of borders & edges within the body by calculated the traversed distance. Ultimately relies on reflection an interface b/w 2 objects is necessary to visualize anything. Most ultrasound transmitters & receivers are packaged in a single unit. They don’t function simultaneously 1 of the objectives of the system is to reduce interference Doppler mode: used to determine the flow of blood within the body by detecting the frequency shift that’s associated with movement toward or away from the receiver. Applications : 1. Therapeutically Ultrasound waves create friction & heat when they act on tissues can increase blood flow to the site of injury in deep tissues & promote faster healing. 2. Focused ultrasound. Focusing a sound wave using a parabolic mirror causes constructive interference at the focal point of the mirror. Creates a v high-energy wave exactly at that point. Can be used to noninvasively break up a kidney stone (lithotripsy) or ablate (destroy) small tumors

  1. Dental cleaning & destruction of cataracts (phacoemulsification). In each case, the ultrasound waves are applied for a sufficient time period to achieve the desired effect. Sources: https://studiousguy.com/doppler-effect-examples/ https://www.pasco.com/resources/blog/ https://www.youtube.com/watch?v=DqwJsa5LiJc