The equation of a wave travelling on a string | vedclass

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(A) The general equation of a wave is $y = A \sin(kx + \omega t + \phi)$.Comparing this with the given equation $y = \sin(20 \pi x + 10 \pi t)$,we get

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(A) The general equation of a wave is $y = A \sin(kx + \omega t + \phi)$.Comparing this with the given equation $y = \sin(20 \pi x + 10 \pi t)$,we get the wave number $k = 20 \pi \ rad/m$.The wavelength $\lambda$ is given by $\lambda = \frac{2 \pi}{k} = \frac{2 \pi}{20 \pi} = 0.1 \ m = 10 \ cm$.Points having the same oscillating speed in a wave are separated by a distance of $\frac{\lambda}{2}$ (or multiples thereof).Therefore,the minimum distance is $\frac{\lambda}{2} = \frac{10 \ cm}{2} = 5 \ cm$.

The equation of a wave travelling on a string is $y = \sin(20 \pi x + 10 \pi t)$,where $x$ and $t$ are distance and time in $SI$ units. The minimum distance between two points having the same oscillating speed is (in $cm$)

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