The function rix, t) = sin [[x - pt]] represens a wave moving C the right along

Question

The function rix, t) = sin [[x - pt]] represens a wave moving C the right along the herizonal axis at a speed of 1.28m/s. Hered = 0.800 mb = 0.625 ml {as Which of the following graphs represents the wave att = 07 Jin) Y(m) 1.0 1. 0.5H " (m) (1) 1 /15 -1.0- -1.0N | AM - INA ACT - RA YIN) (m) 10 1. It 10 1 20/ 30 | 40 (m) -0.5 -0.5H -1.0L -1.0 What is the expression for the wave function ift - 0? At which x values will this wave function have maximum positive y values ? Al which x values will this wave function have maximum negative yvalues!

Explanation / Answer

(a) at t = 0

y(x,t) = a sin(bx)

i.e sin wave without any shift in the x axis

So option 1 is the correct answer

Note-Since option numbers are not given so I am assuming the option numbers as follows-

option1 option2

option3 option4

(b) at t = 2.6 wave equation will be as follows-

y(x,t) = 0.8 sin[0.625*x - (0.625*1.28*2.6)] = 0.8 sin (0.625x - 2.08)

We can see from the expression of y(x,t) that sin function is 0 at x = 2.08/0.625 = 3.33

So option 4 is the most suitable answer

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