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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
answered-by-expert Expert Answer

Progressive wave equation is

img

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

img

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

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velocity of particle at x at time t is determined by differentiating eqn.(2)

img

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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