Waves concept

-Definition of wave:-
It is a disturbance which travels through the medium due to repeated periodic motion of particles of the medium about their equilibrium position.

-Example of wave motion are sound waves traveling through an intervening mediun, water waves, light waves and many more such examples are there.

-Waves requiring material medium for their propagation are called MECHANICAL WAVES. Mechanical waves are governed by Newton's law of motion.

-Sound waves are mechanical waves in atmosphere between source and the listner and require medium for their propagation.

-Other examples of mechanical waves are sesmic waves and water waves.

-Those waves which does not require material medium for their propagation are called NON MECHANICAL WAVES.

-One familiar example of NON MECHANICAL WAVES is waves associated with light or light waves. Another such examples are radio waves, X-rays, micro waves, UV light, visible light and many more.

-Transverse waves are such waves where the displacements or oscillations are perpandicular to the direction of propagation of wave.

-Longitudinal waves are those waves in which displacement or oscillations in medium are parallel to the direction of propagation of wave for example sound waves.

-At any time t , displacement y of the particle from it's equilibrium position as a function of the coordinate x of the particle is
y(x,t)=A sin(ωt-kx)
where,
A is the amplitude of the wave
k is the wave number
ω is angular frequency of the wave
and (ωt-kx) is the phase.

-Wavelength λ and wave number k are related by the relation
k=2π/λ
-Time period T and frequency f of the wave are related to ω by
ω/2π = f = 1/T
-speed of the wave is given by
v = ω/k = λ/T = λf

-Speed of a transverse wave on a stretched string depends on tension and the linear mass density of the string not on frequency of the wave
i.e,
v=√T/μ
T=Tension in the string
μ=Linear mass density of the string

-Sounds waves are longitudinal mechanical waves that can travel through solids,liquid and gases

-Speed of longitudinal waves in a medium is given by
v=√B/ρ
B=bulk modulus
ρ=Density of the medium

-Speed of longitudinal waves in ideal gas is
v=√γP/ρ

P=Pressure of the gas
ρ=Density of the gas
γ=C_p/C_V

Principle of superposition:
When two or more waves traverse thrugh the same medium,the displacement of any particle of the medium is the sum of the displacement that the individual waves would give it.

y=Σy_i(x,t)