Question

The equation of a standing wave produced on a string fixed at both ends at $x=0\text{and}x=L$ respectively is $y=\left(0.8cm\right)\sin \left[\right(0.314cm–1\left)x\right]\cos \left[\right(600\pi s^{-1}$)t]\). Choose the correct statement(s)

• A. The particle of the string at $x=4cm\text{and}x=12cm$ are vibrating in opposite phase
• B. The minimum possible value of $L\text{is}20cm$
• C. The maximum particle speed is $480\pi cm/s$
• D. The particle of the string at $x=5cm\text{and}x=23cm$ are vibrating in same phase

Answer 1

The correct option is A The particle of the string at $x=4cm\text{and}x=12cm$ are vibrating in opposite phase

$\lambda =\frac{2\pi }{K}$
$\lambda =\frac{2\times 3.14}{0.314}=20cm$
Particles between two adjacent nodes vibrate in same phase.