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A transverse hormonic wave on a string o...

A transverse hormonic wave on a string on a string is descibed by
`y(x,t)=3.0sin(36t+0.018x+(pi)/(4))`
Where x and y are in cm and t is in sec. The positve direction of x is from left to rigth .

Text Solution

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The transverse harmonic wave is `y(x,t)=3.0sin[36t+0.018x+(pi)/(4)]`
for x=0,
`y(0,t)=3.0sin(36t+pi//4)`
Here, `omega=(2pi)/(T)=36,T=(2pi)/(36)=(pi)/(18)s`

For different values of t, we calculate y using equation (i). These values are tabulated below : On plotting y versus t graph, we obtained a sinusoidal curve as shown in above figure.

Similar are obtained for x=2 cm and x=4 cm.
The oscillatory motion in travelling wave differs from one point to another only in terms of phase. Amplitude and frequency of oscillatory motion remain the same in all the three cases
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