Waves and Sounds
Wavelength of a standing wave (strings and open pipes)
n is a positive nonzero integer called the harmonic, which corresponds to the number of half-wavelengths supported by the string
open vs closed pipes
open pipe: open at both ends closed pipes: closed at one end and open at the other
loudness (volume of sound)
our perception of intensity
propagation speed of a wave
v=fλ Increased frequency = decreased wavelength = increased pitch Decreased frequency = increased wavelength = decreased pitch
partially constructive and partially destructive interference
waves that are not perfectly in phase or out of phase with each other
sinusoidal waves
waves where the individual particles oscillate back & forth with a displacement that follows a sinusoidal pattern two types: traverse waves and longitudinal waves
harmonic series
a series of frequencies that includes the fundamental frequency and integral multiples of the fundamental frequency
open boundaries
-allow maximal oscillation - places of antinodes - ex: open end of a pipe or free end of a string
Damping or attenuation
-decrease in amplitude of a wave during each oscillation caused by non-conservative forces (friction, air resistance, viscous drag) - doesn't have an effect on the frequency of the wave so the pitch won't change
closed boundaries
-don't allow oscillation -places of nodes -ex: closed end of a pipe or secured ends of a string
sound level
-measured in decibels (dB) I: intensity of the sound wave I0 : threshold of hearing (1 x 10^-12 W/m^2) when intensity of a sound is changed by some factor, one can calculate the new sound level by using the equation Bf = Bi + 10log(If/Ii) where If/Ii is the ratio of the final intensity to the initial intensity
angular frequency
-measured in radians/sec -often used in simple harmonic motion in springs and pendula w=2πf or w= 2π/T
resonating
-oscillating with maximum amplitude - occurs when the frequency of the periodic force is equal to the natural frequency of the system
traveling wave
-when a string fixed at one end is moved up and down, a wave forms and travels toward the fixed end -When the wave reaches the fixed boundary, it is reflected and inverted -If the free end of the string is continuously moved up and down, there will be 2 waves: the original wave moving down the string toward the fixed end and the reflected wave moving away from the fixed end (interfere w/ each other)
normal frequency range of human hearing
20-20,000 Hz
speed of sound in air at 20C
343 m/s
forced oscillation
An oscillation in which a periodic driver force is applied to an oscillator amplitude of a swing become larger and larger because the force frequency is nearly identical to the swing's natural frequency
natural resonant frequency
Frequency at which a system oscillates with greatest amplitude when driven by an external vibrating source. The strongest frequency component emitted when a vibrating body is set into free vibrations
Wavelength
Horizontal distance between the crests or between the troughs of two adjacent waves
ultrasonic waves
Sound waves with frequencies above 20,000 Hz.
infrasonic waves
Sound waves with frequencies below 20 Hz.
Doppler effect
The change in pitch/frequency of a wave as its source moves in relation to an observer if f'>f, the source and detector are moving toward each other if f'<f, the source and the detector are moving away each other for moving away, the sign of velocity is (-) for moving towards, the sign of velocity is (+) ex. ambulance is driving towards an observer from behind. the ambulance is driving toward so Vs is (+). the observer is driving away so Vo is (-). the eq is then f' = f*(V-V0)/(V-Vs)
beat frequency
The difference between the frequencies of the two combining sound waves that make a beat.
sonic boom
The explosive sound heard when a shock wave from an object traveling faster than the speed of sound reaches a person's ears
constructive interference
The interference that occurs when two waves combine to make a wave with a larger amplitude
destructive interference
The interference that occurs when two waves combine to make a wave with a smaller amplitude
overtone vs harmonic
The main difference between harmonics and overtones is that overtones refer to any resonant frequency of a system that has a frequency higher than its fundamental frequency while the term harmonics refer to resonant frequencies which are integer multiples of the fundamental frequency.
shock wave
a cone shaped wave produced by an object moving at supersonic speed through a fluid
pitch
a tone's experienced highness or lowness; depends on frequency high frequency = high pitch low frequency = low pitch
overtone
a vibration whose frequency is a multiple of the fundamental frequency
phase difference
how "in-step" or "out of step" two waves are
displacement
how far a particular point on the wave is from the equilibrium position, expressed as a vector quantity
timbre
quality of sound
standing waves
result from two waves of the same frequency traveling in opposite directions interfere with one another as they travel through the same medium both ends of the string are fixed certain wave frequencies will cause interference between the traveling wave and its reflected wave such that they form a waveform that appears to be stationary the only apparent movement of the string is fluctuations of amplitudes are fixed points along the string points of zero amplitudes are nodes points of max amplitudes are antinodes pipes that are open at both ends can support standing waves pipes that are open at one end but close at another can also contain a standing wave, but because the close end contains a node and the open end contains an antinode, the math is different
speed of sound
sound is a longitudinal wave can travel through solids, liquids, and gases, but not a vacuum v= sqrt(B/p) B: bulk modulus, a measure of the medium's resistance to compression p: density of the medium sound travels fastest through solids and slowest through gases
Doppler ultrasound
study that uses high-frequency sound waves for detection of blood flow within the vessels
intensity
the average rate of energy transfer per area across a surface that is perpendicular to the wave aka power transported per unit area SI unit is watts per square meter (W/m^3) I=P/A P: power A: area intensity is proportional to the square of the amplitude => doubling the amplitude produces a sound that is 4x the intensity intensity is inversely proportional to the square of the distance from the source
fundamental frequency
the lowest frequency of vibration of a standing wave
amplitude
the maximum extent of a vibration or oscillation, measured from the position of equilibrium.
frequency
the number of complete wavelengths that pass a point in a given time measured in Herts (Hz) or cycles per second (cps)
period
the number of seconds one cycle of a wave takes
principle of superposition
when waves interact with each other, the displacement of the resultant wave at any point is the sum of the displacements of the two interacting waves