Question

the displacement produced by a simple harmonic wave is y=10/πsin(200πt-πx/17) then find the time period and maximum velocity of the particle​

Answer 1

Answer:

Given:

Equation of wave

$y = \dfrac{10}{\pi} sin(200\pi t - \dfrac{\pi x}{17} )$

To find:

The time period and the max Velocity of medium particles

Definitions:

Time period is the time taken for the media particles to complete 1 full Oscillations.

Max velocity of the particle means that the maximum velocity with which the media particles perform SHM (oscillatory motion) . The max velocity is obtained at the mean position.

Calculation:

Comparing with a standard Equation of wave :

y = A sin(ωt - kx),

we get ω = 200π and k = π/17

So, Time period

$= \dfrac{2\pi}{ \omega}$

$= \dfrac{2\pi}{200\pi} \\ = \frac{1}{100} \\ = 0.01 \: sec$

Now , differentiation of the wave Equation :

$\therefore \: v = \dfrac{ \delta y}{ \delta t} \\ = > v = \dfrac{10}{\pi} \times 200\pi \: cos(200\pi t - \frac{\pi x}{17} )$

So max Velocity corresponds to max value of cos function that is 1

$= > v = \dfrac{10}{\pi} \times 200\pi \times 1$

$= > v = 2000 \: m \: {s}^{ - 1}$

Answer 2

T = 0.01 sec

V = 2000 m/s

thanks