One end of a `2.4 - m`string is held fixed and the other end is attached to a weightless ring that can slide along a frictionless rod as shown in Fig. 7.86. The three longest possible wavelength for standing waves in this string are respectively

Options

A. `4.8 m , 1.6 m and 0.96 m`
B. `9.6 m , 3.2 m and 1.92 m`
C. `2.4 m , 0.8 m and 0.48 m`
D. `1.2 m , 0.4 m and 0.24 m`

Answer

B

Explanation

When the end of the string is free to move , the string being attached to weightless ring that can slide freely along the rod , the phase of reflected pulse is unchanged antinode is formed at the ring.
`l = (lambda)/( 4) rArr lambda_(1) = 4 l = 9.6 m`
`lambda_(2) = ( 4l)/( 3) = 3.2 m`
`lambda_(3) = ( 4l) /( 5) = ( 9.6)/( 5) = 1.92 m`