Waves and Sound Flashcards
Wave
A disturbance in some medium in which the parts of the medium are displaced and the displacement changes with time due to interactions between the parts
Travelling wave
A disturbance that travels in some direction with a particular speed
Transverse wave
A wave in which the displacement is perpendicular to the direction of travel of the wave
- wave on a string
- wave on water
Longitudinal wave
A wave in which the displacement is in the same direction that the sound wave is travelling in
- slinky waves
- sound waves
Snapshot graph
Shows the displacement as a function of the position along the wave at a specific time
History graph
Shows the displacement at one location as a function of time
Determines the sound that we hear (the sound wave at the location of our ear)
Sinusoidal waves
Waves with a sinusoidal shape (history graph)
Caused by simple harmonic oscillations
Wavelength of a sinusoidal wave
The distance in space between neighbouring peaks
Frequency/period of a sinusoidal wave
The frequency/period of oscillation for any point on the wave
Wave speed
The rate at which the features of a wave travel in the direction that the wave is moving
How are wavelength, frequency/period, and wave speed related?
Pressure
In a gas, the force that it exerts per unit of area
Measured in Pascals
1 Pascal = 1 Newton per square metre
Standard atmospheric pressure
100,000Pa / 100kPa
Force of a gas on a surface
F = P A
Force, pressure, area
Density of molecules & pressure
Molecules per unit volume
Pressure is proportional to density of molecules (for a fixed temperature)
How does a microphone work?
A membrane vibrates in response to the changes in pressure caused by a sound wave
The microphone converts the displacement of the membrane as a function of time to a recordable electrical signal
How does a speaker work?
A speaker converts electrical signals into the motion of an object that displaces the air molecules to create a sound wave
The principle of superposition
Multiple sound waves can travel in the same medium without disturbing each other
The net displacement due to a combination of waves is the sum of the displacements that each wave would have individually
Fourier’s theorem
Any periodic time graph can be decomposed as a sum of sinusoidal time graphs with frequencies f, 2f, 3f, 4f, etc.
Any musical tone (f) is equivalent to a combination of pure tones with frequencies f, 2f, 3f, 4f, etc.
f: the fundamental
2f: the second harmonic
3f: the third harmonic
What is the difference between musical and non-musical sounds?
Non-musical sounds can also be understood as a combination of pure tones, but they generally involve a wide range of frequencies
Spectrum
The information about the pure-tone frequencies present in a sound and the amount of each
Spectrum graph
Shows the amplitude of each frequency of pure tone present in a sound
Standing wave
A combination of a travelling sinusoidal wave moving to the left and a travelling sinusoidal wave with the same wavelength moving to the right, superimposed
Has a sinusoidal shape which simply oscillates up and down
Nodes and antinodes remain in the same place
Nodes
Constant places in a standing wave with zero displacement (while rest of wave oscillates up and down)
On a stretched string fixed at both ends, a node must be at both ends
- allowed wavelengths are 2L, L, 2L/3, L/2, etc. (2L divided by any whole number)
In a cylindrical tube, closed ends have a node, and open ends have an antinode
Antinodes
Constant places in a standing wave with maximum displacement (while rest of wave oscillates up and down)
In a cylindrical tube, closed ends have a node, and open ends have an antinode
Wavelengths in a closed-open tube
In a cylindrical tube, closed ends have a node, and open ends have an antinode
4L, 4L/3, 4L/5, etc.
Wavelengths in an open-open tube
In a cylindrical tube, closed ends have a node, and open ends have an antinode
2L, 2L/3, L/2, etc.
How does hearing work?
Pressure variations in sound waves vibrate the eardrum
The eardrum transfers vibration to the ossicles
Vibration is transformed into waves in the fluid and basilar membrane of the cochlea
Each frequency resonates on a specific area of the basilar membrane, sending signals to specific nerve cells
The nerve cells that fire and their rate of firing (caused by amplitude) determine the information that the brain recieves about the spectrum of sound
What range of frequencies can the human ear detect?
20Hz - 20,000Hz
Just noticable difference in frequencies
The minimum amount of change required to be detected 50% of the time
1/2 semitone (lower frequencies) to 1/20th of a semitone (higher frequencies)
Intensity
Measures the amount of energy per time that flows through a unit of area perpendicular to the sound wave
Watts per square metre
Proportional to the square of the amplitude
Volume
Measured by the amplitude of displacement of the air, the size of pressure variations in the wave, or the intensity of the sound wave
Decibel scale
Describes sound intensities relative to the quietest sound we can typically hear (0dB)
+10dB = 10x increase in intensity
+20dB = 100x increase in intensity
Loudness
Subjective perception of volume
Each 10dB increase in intensity is perceived as 2x increase in loudness
For a fixed intensity, perceived loudness depends on frequency
- more intensity required at high or low frequencies to produce the same loudness
- ears are most sensitive around 3000Hz (the fundamental resonant frequency of the ear canal, open-closed tube)
Constructive interference
Two pure tones with the same frequency and amplitude will reinforce each other if oscillating together (in phase)
Destructive interference
Two pure tones with the same frequency and amplitude will cancel each other out if oscillating oppositely (out of phase)
Beat frequency
The difference in the frequency of two pure tones with slightly different frequencies
The two tones will alternate between oscillating in phase and out of phase (reinforcing and cancelling); we perceive this as a single frequency whose loudness varies periodically
The limit of frequency discrimination
The point below which two pure tones with slightly different frequencies are perceived as ONE single tone with a quality of “roughness”
The critical band frequency
The point below which two pure tones with slightly different frequencies are percieved as TWO separate tones with a quality of “roughness”
Above the critical band, we hear two clear tones
Roughness below critical band frequency
The two tones are exciting overlapping regions on the basilar membrane
Associated with dissonance
