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

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`