7. Waves and Sounds Flashcards
What is the difference between:
Transverse Waves
Longitudinal waves
Transverse waves have oscillations of wave particles perpendicular to the direction of the wave propagation (e.g., “the wave,” electromagnetic waves)
Longitudinal waves have oscillations of wave particles parallel to the direction of wave propagation (e.g., sound waves)
What is displacement of a wave?
Displacement (x) in a wave refers to how far a point is from the equilibrium position, expressed as a vector quantity.
MCAT Expertise- even in simple harmonic motion in springs and strings (pendula) are not on the formal content lists for the MCAT, it’s still important to be familiar with the jargon of wave motion because sound and light (electromagnetic radiation) are on those content lists.
What is the difference between:
Constructive interference:
Destructive Interference:
Partially Constructive or deconstructive Interference:
Constructive interference occurs when waves are exactly in phase with each other. The amplitude of the resultant wave is equal to the sum of the amplitudes of the two interfering waves.
Destructive interferences occurs when waves are exactly out of phase with each other. The amplitude of the resultant wave is equal to the difference in amplitude between the two interfering waves.
Partially constructive and partially destructive interference occur when two waves are not quite perfectly in or out of phase with each other. The displacement of the resultant wave is equal to the sum of the displacement of the two interfering waves.
What are traveling waves?
Traveling waves have continuously shifting points of maximum and minimum displacements
What are Standing Waves?
Standing waves are produced by the constructive and destructive interference of two waves of the same frequency traveling in opposite directions in the same space.
What are nodes and antinodes?
Antinodes are points of maximum oscillation
Nodes are points where there is no oscillation.
No-d-es= No Displacement
True or False: sound waves are a prime example of transverse waves.
False. Sound waves are the most common example of longitudinal waves on the MCAT.
How does applying a force at the natural frequency of a system change the system?
The object will resonate because the force frequency equals the natural (resonant) frequency. The amplitude of the oscillation will increase.
Example: glass breaking with singing
If two waves are out of phase at any interval besides 180 degrees, how does the amplitude of the resultant wave compare to the amplitude of the two interfering waves.
If two waves are perfectly in phase, the amplitude of the resulting wave is equal to the sum of the amplitudes of the interfering waves.
If two waves are perfectly out of phase, the amplitude of the resulting wave is the difference of the amplitudes of the interfering waves.
Therefore, if the two waves are anywhere between these two extremes, the amplitude of the resulting wave will be somewhere between the sum and difference of the amplitudes of the interfering waves.
what is the definition of:
Wave Speed:
Frequency:
Angular Frequency:
Period:
Equilibrium Position:
Amplitude:
Wave Speed- Wave speed is the rate at which a wave transmits the energy or matter it is carrying. Wave speed is the product of frequency and wavelength
Frequency- Frequency is a measure of how often a waveform passes a given point in space. It is measured in Hz.
Angular Frequency- Angular frequency is the same as frequency but is measured in radians per second.
Period- Period is the time necessary to complete a wave cycle
Equilibrium position- The equilibrium position is the point with zero displacement in an oscillating system.
Amplitude: Amplitude is the maximal displacement of a wave from the equilibrium position.
What is the definition of wave frequency?
Frequency- Frequency is a measure of how often a waveform passes a given point in space. It is measured in Hz. It determines pitch
What is the definition of wave period?
Period- Period is the time necessary to complete a wave cycle
What is the definition of wave angular frequency?
Angular Frequency- Angular frequency is the same as frequency but is measured in radians per second.
How is sound produced and transmitted?
Sound is produced by mechanical vibrations. These are usually generated by solid objects like bells or vocal cords, but occasionally can be generated by fluids. Sound is propagated as longitudinal waves in matter, so it cannot propagate in a vacuum.
To which properties of a sound wave do amplitude and frequency correspond?
Amplitude: The amplitude of a wave is related to its sound level (volume).
Frequency: frequency of a wave is related to its pitch.
For each of the following diagrams, label the type of pipe or string it represents, a node and antinode, and the relevant equation relating to λ and L
(Equation) What is the equation for the speed of sound in a given medium?
v=Bulk modulus (a measure of the medium’s resistance to compression)
ρ= density of the medium
v= speed
What is the bulk modulus? The relevant elastic property is the bulk modulus, B. This tells us how much a medium’s volume changes when the pressure on it changes.
(Equation) What is the equation for the doppler effect?
f’=is the perceived frequency (Hz)
f= actual emitted frequency (Hz)
v= speed of sound in a medium (340 m/s)
vd= the speed of sound of the detector (you listening to the siren)
vs= speed of the source
Note both the + and – signs. The upper sign (+) should be used when the detector (you) is moving source is moving toward the other object (ambulance). The lower sign should be used when the detector (you) or source is moving away from the other object (ambulance).
(Equation) What is the equation for sound intensity, or loudness?
I= intensity (W/m2)
P= power (Watts)
A= area (m2)
Real world: the power delivered across the surface such as the tympanic membrane is equal to the product of the intensity I and the surface area A, assuming the intensity is uniformly distributed.
(Equation) What is the equation for intensity as it is converted to decibles.
β= sound level, measured in decibels (dB)
I= intensity of the sound
IO= threshold of hearing (1x10-12 W/m2)
What are standing waves? Why are strings and open pipes considered standing waves?
Standing Waves: occurs whenever two waves of the same frequency traveling in opposite directions interfere with one another as they travel through the same medium. They appear to be standing still, not propagating, because the interference of the wave and its reflected wave produce a resultant that fluctuates only in amplitude.
(Equation): What is the equation for the wavelength of a string?
λ= wavelength
L= length
n= the harmonic, which corresponds to the number of half-wavelengths supported by the string (easy way to remember: number of antinodes)
Calculate the wavelengths of the following strings
use equation λ=(2L)/n
A= λ=2L
B= λ=L
C=λ=(2L)/3
(Equation) What is the equation for the pitch of a standing wave of a string?
Pitch is a result of the frequency
f= frequency (Hz)
n= harmonic (number of antinodes)
v= speed of the wave (m/s)
L= length (m)
(Equation) What is the equation for wavelength of a sound wave in a closed pipe?
λ= wavelength of standing wave in closed pipe
L= length
n= the harmonic, which corresponds to the number of half-wavelengths supported by the string. This can only be odd integers (n= 1,3,5 and so on)
(Equation) Frequency or (pitch) of the standing wave in a closed pipe
f= frequency
v= speed of the wave
L= length
n= the harmonic, which corresponds to the number of half-wavelengths supported by the string. This can only be odd integers (n= 1,3,5 and so on)
(Equations): Write out the equation for wavelength and pitch (frequency) for closed pipes and strings.
