Waves Flashcards
Wave Motion
Kind of disturbance which travels through a medium due to repeated vibrations of the particles of the medium about their mean positions
Propagation of Sound Waves through Air
- A small region in air is likes a spring - As it travell through the air, it compresses or expands it
- If a region is compressed, density increases of the second region causeing the first region density to decrease
- This causes rarefaction and hence shifts it to adjacent region
Propagation of sound in a solid
- When an eleastic wave propagates, the atom is displaced from its equilibrium position and a restoring force is developed
Transverse Waves
- Waves in which the individual particles of the medium oscillate perpendicular to the direction of wave propagation
- Travel through a liquid medium
Longitudinal Waves
- Waves in which the individual particles of the medium oscillate along the direction of wave propagation
- Travel through all media
Angular Frequency
Rate of change of phase with time
Wavelength
Distance covered by a wave during the time in which a particle of the medium completes one vibration to and fro about its mean position
Angular wave number / Propagation constant
Quantity 2pi / lambda (phase change per unit path difference)
Wave velocity / Phase velocity
Direction covered by a wave per unit time in its direction of propagation
Speed of transverse wave on stretched string
v = root (T / m)
Speed of a transverse wave in a solid
v = root (modulus of rigidity (aka shear modulus) / ro)
Speed of longitudinal Wave in a liquid or gas
v = root (k / ro)
k = bulk modulus
Speed of longitudinal wave in a solid
root (k + 4/3 * shear modulus) / ro)
Speed of a longitudinal wave in a solid rod
v = root (Y / ro)
Newton’s Formula for speed of sound in a gas
v = root (P / ro)
Laplace formula for speed of sound in a gas
v = root (gamma * P / ro)
gamma = Cp / Cv
Plane Progressive harmonic wave
If during the propagation of a wave through a medium, the particles of the medium vibrate simple harmonically about their mean positions, then the wave is said to be plane progressive
Factors which affect speed of sound in a gas
- Pressure has no effect!
- At constant pressure, v inversely proportional to square root of density
- Travels faster in moist air than dry hair
- Directly proportional to square root of abs. temp
Progressive Wave
Wave that travels from one point of the medium to another
Angular wave number or Propagation constant
k = 2pi / lambda
y(x,t) =
A sin (omega t - kx)
= A sin 2 pi(t / T - x / lambda)
= A sin 2pi/T (t - x / v) = A sin 2pi / lambda (vt - x)
Explain Progressive wave
y = A sin (omega t - kx + psi not)
y = Displacement
A = amplitude
omega = angular freq
t = time
k = angular wave number
x = position
psi not = initial phase angle
Phase of a wave
Quantity that gives complete information of the wave at any time and at any position
Time period of a wave
Time in which the phase of a particle of the medium changes by 2pi
Wavelength
Distance between two points which have a phase difference of 2pi at any given instant
Particle velocity
Velocity with which the particles of the medium vibrate about their mean positions
Wave velocity
Distance covered by a wave in the direction of its propagation per unit time
Acceleration amplitude / maximum value of acceleration
a = (2pi / T)^2
Particle Acceleration
acceleration (rate of change in speed and direction) of particles
Displacement along negative x-axis
y = A sin (omega t + kx)
phase formula
2pi (t / T - x / lambda) + psi not
Reflection of a wave from a rigid body
It is reflected back with a phase reversal or phase difference of pi radians
Reflection of a wave from an open boundary
Suffers no phase change
Antinode
An antinode wave is a point on a standing wave where the amplitude of the wave is at its maximum
Waves during refraction from one medium to another
Suffers no phase change
Principle of superposition of waves
When a number of waves travel through a medium simultaneously, the resultant displacement of any particle of the medium at any given time is equal to the algebraic sum of the displacements due to individual waves
Constructive interference
When two waves travel in the same direction and are in phase with each other, their amplitude gets added, and the resultant wave is obtained.
Destructive interference
- Destructive interference occurs when waves come together so that they completely cancel each other out.
- Same amplitude in opposite directions
Stationary waves
When two identical waves of same amplitude and frequncy travelling in opposite directions with the same speed along the same path superpose each other, the resultant wave does not travel in the either direction
Equation of stationary wave
y = (2A cos kx) sin omega t
Characteristics of stationary waves
- Disturbance does not advance forward
- All particules, except at nodes, execute SHM
- Nodes and antinodes
- Distance between two successive nodes is lambda / 2
- Amplitudes different at different points
- Has same wavelength and time period as two component waves
Comparison between stationary and progressive waves
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First harmonic / Fundamental frequency
The first harmonic, also known as the fundamental frequency, is the lowest frequency at which a string or air column can vibrate to create a standing wave pattern
Normal Modes
A normal mode of a dynamical system is a pattern of motion in which all parts of the system move sinusoidally with the same frequency and with a fixed phase relation
Sinusoidally
Sinusoidally means relating to, shaped like, or varying according to a sine curve or sine wave
Velocity when it vibrates in p segments
Vp = p / 2L (root (T / m))
A pipe of length L with one end closed and other end open vibrates with frequencies given by
v = (n + 1/2) mu / 2L
Fundamental mode / First harmonic is v = mu / 4L
Beats
Periodic variations in the intensity of sound caused by the superposition of two sound waves of slightly different frequencies
Beat frequency
Difference in frequencies of two superposing waves (v1 - v2)
