Question

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

• A. $1.2$ m/s
• B. $1.7$ m/s
• C. $2.9$ m/s
• D. $3.4$ m/s

Answer 1

The correct option is C $2.9$ m/s

$y(x,t)=\left(2.20cm\right)sin\left[\right(13rad/s)t+(15rad/m\left)x\right]{\left(\frac{\partial y}{\partial t}\right)}_x=\left(2.20cm\right)cos\left[\right(13rad/s)t+(15rad/m\left)x\right]\cdot \left(130rad/s\right)$

$\downarrow$

Differentiation of $y$ wrt ${}^{\prime }{t}^{\prime }$, keeping $x$ constant

To find maximum transverse speed,

${\left(\frac{\partial y}{\partial t}\right)}_x$ has to be maximum, this will be maximum when $cos\left[\right(13rad/s)t+(15rad/m\left)x\right]=1$

$\therefore$ Max. transverse speed $=\left(2.20cm\right)\times \left(130rad/s\right)=286cm/sec=2.86m/sec$

Approximate speed $=2.90m/s$