Question

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

• A. The number of nodes is $5$ ,
• B. The length of the string is $0.25\, m$.
• C. 3.3 $\times 10^{-11}\,Wb$ The maximum displacement of the midpoint of the string its equilibrium position is $0.01 \,m$.
• D. The fundamental frequency is $100 \,Hz$.

Answer 1

Answer: (B), (C)

(A) There are $5$ complete loops. Total number of nodes $=6$
(B) $\omega=628 sec ^{-1}$
$k =62.8 \,m ^{-1}=\frac{2 \pi}{\lambda} \Rightarrow \lambda=\frac{1}{10}$
$V_{w}=\frac{\omega}{k}=\frac{628}{62.8}=10 \,ms ^{-1} $
$ L =\frac{5 \lambda}{2}=0.25$
(c) $2 A =0.01=$ maximum amplitude of antinode