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Question

A transverse wave on a string is described by the equation y(x,t)=(2.20 cm)sin[(130 rad/s)t+(15 rad/m).x], then find the approximate maximum transverse speed of a point on the string.

A
1.2 m/s
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B
1.7 m/s
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C
2.9 m/s
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D
3.4 m/s
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Solution

The correct option is C 2.9 m/s
y(x,t)=(2.20cm)sin[(13rad/s)t+(15rad/m)x](yt)x=(2.20cm)cos[(13rad/s)t+(15rad/m)x](130rad/s)
Differentiation of y wrt t, keeping x constant

To find maximum transverse speed,
(yt)x has to be maximum, this will be maximum when cos[(13rad/s)t+(15rad/m)x]=1

Max. transverse speed =(2.20cm)×(130rad/s)=286cm/sec =2.86m/sec

Approximate speed =2.90m/s

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