The displacement of the particle at x = 0 of a stretched string carrying a wave in the positive x -direction is given by $f (t) = A sin (t / T) .$ The wave speed is v. Write the wave equation.

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Solution

At $x = 0, f (t) = a sin (t / T)$
Wave speed = v
$\Rightarrow λ =$ wavelength $= v T$ (T = times period)
So, general equation of wave
$Y = A sin [(t / T) - (x / v T)]$ [because $y = f ((t / T) - (x / λ))$

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The displacement of the particle at x = 0 of a stretched string carrying a wave in the positive x -direction is given by f(t)=Asin(t/T). The wave speed is v. Write the wave equation.

At x=0,f(t)=asin(t/T)Wave speed = v⇒λ= wavelength =vT (T = times period)So, general equation of waveY=Asin[(t/T)−(x/vT)] [because y=f((t/T)−(x/λ))

The displacement of the particle at x = 0 of a stretched string carrying a wave in the positive x -direction is given by $f (t) = A sin (t / T) .$ The wave speed is v. Write the wave equation.

At $x = 0, f (t) = a sin (t / T)$
Wave speed = v
$\Rightarrow λ =$ wavelength $= v T$ (T = times period)
So, general equation of wave
$Y = A sin [(t / T) - (x / v T)]$ [because $y = f ((t / T) - (x / λ))$