Question

The equation of a plane progressive wave is y = 0.09sin8 `pi` `["t" - "x"/20]`.When it is reflected at a rigid support, its amplitude becomes `2/3`rd of its 3 previous value. The equation of the reflected wave is ______.

Options

• y = - 0.09 sin 8 `pi` `["t" - "x"/20]`

• y = 0.06 sin 8 `pi` `["t" - "x"/20]`

• y = 0.06 sin 8 `pi` `["t" + "x"/20]`

• y = - 0.06 sin 8 `pi` `["t" + "x"/20]`

Answer 1

The equation of a plane progressive wave is y = 0.09sin8 `pi` `["t" - "x"/20]`.When it is reflected at a rigid support, its amplitude becomes `2/3`rd of its 3 previous value. The equation of the reflected wave is y = - 0.06 sin 8 `pi` `["t" + "x"/20]`.

Explanation:

New amplitude = 0.09 `xx 2/3` = 0.06

Direction is reversed.

Thus required equation will be

y = - 0.06 sin 8 `pi` `["t" + "x"/20]`