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Mechanical Waves:
A disturbance which propagates through a medium with little or no net displacement of the particles of the medium.
Velocity and Frequency:
The distance traveled by a given point on the wave (such as a crest) in a given interval of time
V=d/t d: distance (m) T: time (s)
V=(wavelength)(frequency)
The period T is the time to move a distance of one wavelength.
V=l/T but T=1/f
Wave Types:
Transverse Waves: a wave in which particles of the medium move in a direction perpendicular to the direction that the wave moves (string).
Longitudinal Waves: a wave in which particles of the medium move in a direction parallel to the direction which the wave moves. These are also called compression waves (sound).
-Other types are Combination, Surface, and Electromagnetic
Reflection:
Occurs when a wave strikes a medium boundary and “bounces back” into original medium.
Completely reflected waves have the same energy and speed as original wave.
TYPES:
Fixed-end reflection: the wave reflects with inverted phase
Open-end reflection: the wave reflects with the same phase
Refraction:
Occurs when a wave strikes a medium boundary and is forced to change speeds relative to the original medium
The approaching wave is partially transmitted and partially reflected.
Refracted waves may change speed and therefore wavelength, too.
The energy of the approaching wave may be split at the boundary.
Is almost always accompanied by some reflection
Does not change frequency
Interference:
When two or more waves pass a particular point in a medium simultaneously, the resulting displacement at that point in the medium is the sum of the displacements due to each individual wave. The waves interfere with each other.
Types of Interference:
Constructive: if the waves are “in phase” (crests and troughs aligned), the amplitude is increased.
Destructive: waves are “out of phase.” The amplitude is decreased and can even be zero.
Sound is a longitudinal wave:
Travels through the air at approximately 340m/s
Is started by vibrations of some other material, which starts the air moving.
Intensity and Loudness:
Sound intensity is defined as the sound power per unit area.
I=P/A A=(4)(3.1415)(r)
P = power A = Area
Sound Loudness is the physical strength of a sound directly influenced by its amplitude.
B=10Log(I/Io)
B=Loudness I=Intensity of wave Io=1.0e12
Resonance:
Occurs when a vibration from one oscillator occurs at a natural frequency for another oscillator. The first will cause the second to vibrate.
Wave Speed in a String:
The wave speed v in a vibrating string is determined by the tension F and the linear density (u thing), or mass per unit length.
V=(square root)F/u thing V=(square root)FL/m
Energy of a Periodic Wave:
The energy of a periodic wave in a string is a function of the linear density m, the frequency f, the velocity v, and the amplitude A of the wave.
E/L=2(3.14)2f2A2u P=2(3.14)2f2A2uv
Standing Wave:
A wave which is reflected back and forth between fixed ends
Reflection may be fixed or open-ended
Superposition of the wave upon itself results in a pattern of constructive and destructive interference and an enhanced wave.
Formation of a Standing Wave:
Incident and reflected waves traveling in opposite directions produce nodes N and antinodes A.
The Distance between alternate nodes and antinodes is the wavelength.
Possible Wavelengths for Standing Waves:
Fundamental, n=1
1st Overtone, n=2
2nd Overtone, n=3
n=harmonics
l=2L/n n=1,2,3,…
Possible Frequencies f=v/l
fn=nv/2L n=1,2,3,…
Characteristic Frequencies:
fn=n/2L (square root)F/u n=1,2,3,…
Doppler:
The raising and lowering of the perceived pitch of a sound based on the relative motion of observer and source of the sound.
Open-end Standing Waves:
Fixed-end Standing Waves:
Mixed Standing Waves:
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