The equation for the fundamental standing sound wave in a tube that is closed at both ends if the tube is `80 cm` long and speed of the wave is `330 m//s` is (assume that amplitude of wave at antinode to be `s_(0)`)

Options

A. `y = s_(0) cos (3.93 t) sin (1295 x)`
B. `y = s_(0) sin (7.86 t) cos (1295 x)`
C. `y = s_(0) cos (7.86 t) sin (1295 x)`
D. `y = s_(0) cos (1295 t) sin (3.93 x)`

Answer

D

Explanation

Since `f_(n) = n ((v)/( 2 L)) = n((330)/( 1.6)) = 206 n`
`lambda_(n) = ( 2 L)/(n) = (1.6)/(n)` `{ L = (n lambda_(n))/(2)}`
And the standing wave equation with nodes at both ends is
`s = s_(0) sin(3.93 n x) cos (1295 n t)`
For fundamental mode//frequency ` n = 1`
`s = s_(0) = sin (3.93 x) cos (1295 t)`