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y=1mm sin pie(x/2cm-t/0.01s)
find equation of velocity
speed of x=1cm,t=0.01
speed of x=3cmt=0.01
speed of x=5cm,t=0.01
speed of x=7cm,t=0.01
Asked by btennyson663 | 13 Jun, 2024, 20:02: PM
Expert Answer
Progressive wave equation is
where y is displacement of particle at x and at time t , A is amplitude, λ is wavelength and T is period .
Given wave equation is
By comparing eqn.(1) and (2) , we get
Amplitude A = 1 mm
Wavelength λ = 4 cm
Period T = 0.02 s
Frequency f = 1/T = 50 Hz.
------------------------
Velocity of wave , v = f λ = 50 × 0.04 m/s = 2 m/s
-------------------------------------
velocity of particle at x at time t is determined by differentiating eqn.(2)
velocity at x = 1 cm and at t = 0.01 s is determined by substituting the relevant values in eqn.(3)
we get , v(1 cm , 0.01 s ) = 0
Similarly we get velocty at various values of x and t from eqn.(3)
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