Question

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

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

Answer 1

Answer: (B), (C)

The correct options are
B the length of the string is $0.25m$.
C The maximum displacement of the midpoint of the string from its equilibrium position is $0.01m.$

$20{\pi }^{=}\frac{2\pi }{\lambda }$
$\lambda =\frac{1}{10}m=0.1m$
length of the spring $=0.5\times \frac{1}{2}=0.25m$
Mid point is the antinode
Frequency at this mode is $f=\frac{200\pi }{2\pi }=100Hz$
Fundamental frequency $=\frac{100}{5}=20Hz$

Therefore, correct options are $B$ and $C$