Question

The equation of a stationary wave is given by 2 sin `((pi"x")/15) "cos" (48 pi"t").`The distance between a node and its next antinode is ____________.

Options

• 22.5 units

• 7.5 units

• 30 units

• 1.5 units

Answer 1

The equation of a stationary wave is given by 2 sin `((pi"x")/15) "cos" (48 pi"t").`The distance between a node and its next antinode is 7.5 units.

Explanation:

`"Y" = 2  "sin" ((pi "x")/15) "cos" (48 pi"t")`

`therefore "k" = pi/15`

`therefore (2pi)/ lambda = pi/15 Rightarrow lambda = 30  "units"`

Distance between a node and its next antinode is

`lambda/4 = 30/4 = 7.5  "units"`