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CHAPTER 10: MECHANICAL WAVES, EXAMPLE, K : the wave number, a : the…
CHAPTER 10: MECHANICAL WAVES
Progressive wave:
y=Asin(ωt+-kx)
Velocity of a particles
y=Aωcos(ωt+-kx)
Acceleration of particle:
y=-Aωsin(ωt+-kx)
y=-ω²y
y vs t
y vs x
intro
wave - disturbance produce in a medium due to the periodic vibrations of the particles of the medium abt their equilibrium position
wave transfer energy from one point to another without transporting any particle btwn any 2 points
wave and energy
electromagnetic waves
transportation of energy because of the disturbance in electric and magnetic fields
can propogate in vacuum
combination of electrical and magnetic waves
electromagnetic waves is produced by accelerating electric charge
mechanical wave
defined as a disturbance tht travels thru particles of the medium to transfer the energy
the particles oscillate around their equilibrium position but do not travel
Differences between progressive and stationary waves
did they move?
In progressive waves, wave profile move.
In stationary waves, wave profile does not move.
how do they vibrate?
In progressive waves, all particle vibrates with same amplitude
In stationary waves, particle between two adjacent nodes vibrate in phase
transmissions of energy
In progressive waves, energy is transmitted
In stationary waves, energy does not transmitted
how they being produced?
Progressive waves produced by a disturbance in an elastic medium
Stationary waves produced by superposition of two waves moving in opposite direction
STATIONARY (STANDING WAVE)
Formed when two waves similar in speed, frequency and amplitude but different in opposite direction are superimposed
A stretched string between two supports that is plucked like a guitar or violin string
Definition - A form of wave in which the profile of the wave does not move through the medium.
type of wave
longitudinal w.
direction of vibration parallel to the direction of the propagation
example
sound wave
wave in spring
transverse w.
its direction of vibrations of the particle is perpendicular to direction of wave propagation
example
water wave
e.m. wave
wave on string( rope)
SUPERPOSITION OF WAVES
principle of superposition
Resultant displacement by 2 waves at a point is
the vector sum of the individual displacement
types of superposition
destructive interference
constructive waves
3 different cases
two waves of
slightly different frequencies
traveling in the
same direction
,giving rise to
phenomenon of beats.
of two waves of
same frequency
and
same amplitude
moving in
opposite directions
,giving rise to
standing waves or stationery waves
same frequency
traveling in the
same direction
giving rise to a
sustained interference pattern
.,
properties of wave
progressive wave
wave tht propagate continuously outwards from a source of disturbance
stationary/standing w.
The equation of Stationary Wave :
x : distance traveled by wave
y = 2 a cos kx sin ωt where, amplitude of stationary wave = 2a cos kx
node to antinode = λ/4
node to node =λ/2
y2 = a sin ( ωt - kx )
y1 = a sin (ωt + kx )
EXAMPLE
When the string is plucked
Progressive waves is produced in both directions
At the end of the string
The waves will be reflected and travel back in opposite direction
K : the wave number
a : the amplitude of the progressive wave
ω : the angular frequency
(+ve)=left
(-ve)=right
