A wave pulse is travelling on string in +x direction.The shape of a string at t=0 is given by f(x)=Asin( x/a),where `A`and`a`are constant.If wave speed is v,write the wave equation.

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Solution

$f (x) = A \sin (\frac{x}{a}) wave equation is given by : y = A \sin (kx - ωt) k = \frac{1}{a} v is the velocity and we know v = \frac{ω}{k} ω = vk = \frac{v}{a} Y = A \sin (\frac{x}{a} - \frac{v}{a} t) Y = A \sin (\frac{1}{a} (x - vt))$

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A wave pulse is travelling on string in +x direction.The shape of a string at t=0 is given by f(x)=Asin( x/a),where `A`and`a`are constant.If wave speed is v,write the wave equation.

f(x) = A sinxawave equation is given by:y = A sinkx-ωtk = 1av is the velocityand we knowv = ωkω = vk = vaY = A sinxa-vatY = A sin1ax-vt

$f (x) = A \sin (\frac{x}{a}) wave equation is given by : y = A \sin (kx - ωt) k = \frac{1}{a} v is the velocity and we know v = \frac{ω}{k} ω = vk = \frac{v}{a} Y = A \sin (\frac{x}{a} - \frac{v}{a} t) Y = A \sin (\frac{1}{a} (x - vt))$