A horizontal stretched string, fixed at two ends, is vibrating in its fifth harmonic according to the equation, `y(x,t)=(0.01m)sin[(62.8m^(-1))x]cos[628s^(-1))t]`. Assuming `pi=3.14`, the correct statements (s) is (are)

Options

A. The number of nodes is `5`.
B. The length of the string is `0.25 m`
C. The maximum displacement of the midpoint of the string its equilibrium position is `0.01 m`.
D. The fundamental frequency is `100 Hz`.

Answer

B,C

Explanation

(A) There are `5` complete loops.
Total number of nodes `= 6`
(B) `omega = 628 sec^(-1)`
`k = 62.8 m^(-1) = (2pi)/(lambda) rArr lambda = (1)/(10)`
`v_(w) = (omega)/(k) = (628)/(62.8) = 10 ms^(-1)`
`L = (5lambda)/(2) = 0.25`
(C) `2A = 0.01 =` maximum amplitude of antinode
(D) `f = (v)/(2l) = (10)/(2 xx 0.25) = 20 Hz`.