A string has linear mass density `m = 0.1 kg // m`. A `L = 60 cm` segment of the string is clamped at A and B and is kept under a tension of `T = 160 N` [The tension providing arrangement has not been shown in the figure]. A small paper rider is placed on the string at point R such that `BR = 20 cm`. The string is set into vibrations using a tuning fork of frequency `f`.
(a) Calculate all values of f below `1000 Hz` for which the rider will not vibrate at all.
(b) Calculate all values of f below `1000 Hz` for which the rider will have maximum oscillation amplitude among all points on the string.

Answer

(a) `100, 200, 300…….900 Hz`
(b) it is not possible to have antinode at R