Question

A transverse wave y =0.05 sin (20πx - 50πt) in metre, is propagating along +ve X-axis on a
string. A light in insect starts crawling on the string with the velocity of 5 cms at t = 0 along
+ve X-axis forn a point where x = 5 cm. After 5s the difference in the phase of its position is
equal to
(a) 150π
(b) 250π
(c) 10π
(d) 5π
​

Answer 1

Given:

• Transverse wave  $y =0.05 \ sin (20\pi x - 50\pi t)$ is propagating along $+ve \ X-axis$on a  string.
• A light in insect starts crawling on the string with the velocity $= 5 cms^{-1}$ at $t = 0$ along  $+ve \ X-axis$  form a point $where \ x = 5 cm$.

To Find:

• After $5s$ the difference in the phase of wave position.

Solution:

          $y =0.05 \ sin (20\pi x - 50\pi t)$

At $t=0$ and $x = 5cm$

Initial phase

        $\phi_{i} = 20\pi \times 5 - 50 \pi (0)$

        $\phi_{i} = 100 \pi$            ...........................................$eq_(i)$

After $5s$

       $Distance(D) = V \times t$

                            $= 5 \times 5\\= 25cm$

Now, $x = 25 + 5 = 30cm$

         $t = 5s$

Final phase

       $\phi_{i} = 20\pi \times 5 - 50 \pi (0)$

       $\phi_{i} = 350\pi$    ...........................................$eq_(ii)$

Phase difference

      $\phi = \phi_{f} - \phi_{i}$

Putting the values

      $\phi = 350\pi-100\pi$

      $\phi = 250\pi$

Thus, The phase difference after $5s$ $is \ 250\pi$