Question

The equation of the standing wave in a string clamped at both ends, vibrating in its third harmonic is given by : $y=0.4\sin \left(0.314x\right)\cos \left(600\pi t\right)$ where, $x$ and $y$ are in cm and $t$ in sec.

a) the frequency of vibration is $300Hz$
b) the length of the string is $30cm$
c) the nodes are located at $x=0,10cm,30cm$

• A. a,b
• B. a,c
• C. b,c
• D. a,b,c

Answer 1

The correct option is D a,b,c

$\sin \left(0.314x\right)=0$
$\Rightarrow 0.314x=K_2\pi =K\times 3.14$
$x=10k$
$\therefore$ nodes are at $0,10,20,30cm$
$2\pi f=600\pi$
$\Rightarrow f=300H_z$
length $l=\frac{3\lambda }{2}=3\left(10\right)=30cm$