A string fixed at both ends is vibrating in the lowest possible mode of vibration for which a point at quarter of its length from one end is a point of maximum displacement. The frequency of vibration in this mode is 100 Hz. What will be the frequency emitted when it vibrates in the next mode such that this point of maximum displacement?

Explanation

Since the mode has an antinode at `1//4` point
`I//4 = lambda//4 or I = lambda and 100 = ( c )/( T)` `( c = n lambda)`
In the next mode , between the nearest end `1//4` point from this end , there must appear one node and antinode.
`:. I//4 = ( 3 lambda')/(4) where lambda'` is the wavelength of the next mode
`rArr lambda' = I//3`
`:. n' = (c )/( I//3) = (3 c )/(I) = 3 xx 100 = 300 Hz`