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