Question

explain me the topic DISPLACEMENT IN A TRAVELLING WAVE of class 11 ... don't copy from google

Answer 1

Displacement in a progressive wave

Amplitude and phase together describe the complete displacement of the wave.

• Displacement function is a periodic in space and time.
• Displacement of the particles in a medium takes place along the y-axis.
• Generally displacement is denoted as a function of X and T, but here it is denoted by y.
• In case of transverse wave displacement is given as:
• y(x,t) where x=propagation of the wave along x-axis, and particles oscillates along y-axis.
• Therefore y(x,t)= A sin(kx – ωt + φ).This is the expression for displacement.
• This expression is same as displacement equation which is used in oscillatory motion.
• As cosine function;y(x,t)= B cos(kx – ωt + φ),As both sine and cosine function)y (x, t) = A sin (kx – ωt + φ) + B cos(kx – ωt + φ)
• Mathematically:
• Wave travelling along +X-axis: y(x, t) = a sin (kx – ωt + φ).
• Consider y=asin(kx – ωt + φ)=> y/a=sin(kx – ωt + φ)
• sin-1(y/a) = kx-ωt =>kx=sin-1(y/a) +ωt
• x=(1/k)sin-1(y/a)+ (ωt/k)
• Wave travelling along –X-axis: x=(1/k)sin-1(y/a)-(ωt/k)(only change in the sign ofωt)
• Conclusion:-
• As time t increases the value of x increases. This implies the x moves along x-axis.
• As time t decreases the value of x decrease. This implies the x moves along (-)ive x-axis.

Answer 2

Particle displacement or displacement amplitude is a measurement of distance of the movement of a sound particle from its equilibrium position in a medium as it transmits a sound wave. The SI unit of particledisplacement is the metre (m).