A horizontal stretched string, fixed at two ends, is vibrating in its fifth harmonic according to the equation, `y(x,t)=(0.01 m) sin[(62.8 m^(-1)x] cos[(628 s^(-1))t]`. Assuming `p = 3.14`, the correct statement(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, from its equilibrium position is 0.01 m
D. The fundamental frequency is 100 Hz

Answer

B, C

Explanation

`y=(0.01)msin[(62.8m^(-1))xx]cos[(628s^(-1))t]`
for `5^(th)` harmonic
`5(lambda)/(2)=1`
`k=(2pi)/(lambda)implies 62.8=(2pi)/(lambda) implies lambda=(2pi)/(62.8)m`
`implies 1=5/2xx(2pi)/(62.8)=5/2xx(2xx3.14)/(62.8)=1/4m=0.25m`
Number of nodes=6
At mind point string there is an antinode
`y_(max)` at midpoint=0.01m
`f_0=(v)/(2 1)=(omega//k)/(2 1)=(628//62.8)/(2xx0.25)=10/0.5=20Hz`