Question

A horizontal is string fixed at two ends, is vibrating in its fifth harmonic according o 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), (D)

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 $0.01m$
D The fundamental frequency is $100Hz$.

For horizontal string fixed at two ends

$v=\frac{nV}{2L}$

$4\left(x_{1}t\right)=0.01m\sin \left(62.8x\right)\cos \left(628t\right)$

$w=2\pi v=628$

$v=100H_2$

$\frac{2\pi }{\lambda }=62.8$

$\lambda =0.1m$

From fig above length of string

$=2.5\lambda =2.5\times 0.1=0.25m$

No of Nodes $=6$ from the fig above

Since amplitude $=0.01m$ max displacement is same hence Option $A$ is incorrect $BCD$ is correct.