Question

the equation of transverse wave along a stretched string y=5sinπ÷2(100t-x)in CGS unit the time period of wave is​

Answer 1

Given:

The equation of transverse wave along a stretched string in CGS unit;

$\boxed{y = 5 \sin \bigg \{ \dfrac{\pi}{2} (100t - x) \bigg \} }$

To find:

Time period of wave.

Calculation:

Time period of a progressive transverse wave is the time taken by a specific medium particle to complete 1 full oscillation.

$y = 5 \sin \bigg \{ \dfrac{\pi}{2} (100t - x) \bigg \}$

$= > y = 5 \sin(50\pi t - \dfrac{\pi x}{2})$

Comparing the given Equation with a general Equation:

$\boxed{y = a \sin( \omega t - kx) }$

$\therefore \: \omega = 50\pi$

Therefore let time period be T ;

$\therefore \: T = \dfrac{2\pi}{ \omega}$

$= > \: T = \dfrac{2\pi}{50\pi}$

$= > \: T = \dfrac{2}{50}$

$= > \: T = 0.04 \: sec$

So, final answer is:

$\boxed{ \sf{\: T = 0.04 \: sec}}$