Question

A standing wave is formed by the interference of two travelling waves, each of which has an amplitude $A=\pi cm$, angular wave number $k=\left(\pi /2\right)$ per centimetre. What is the amplitude of the standing wave at $x=0.50cm$ from a node ?

• A. $\sqrt{3}\pi cm$
  
• B. $\sqrt{2}\pi cm$
  
• C. $\sqrt{7}\pi cm$
  
• D. $\sqrt{9}\pi cm$
  

Answer 1

The correct option is B $\sqrt{2}\pi cm$

For a standing wave of form $y=2Asin\left(kx\right)cos\left(\omega t\right)$

$k=\frac{2\pi }{\lambda }$, $A$ is the amplitude of interfering waves

Maximum displacement of a point at $x=0.5cm$ from node=Amplitude of the wave at that point=$2Asin\left(kx\right)=2\pi sin(\frac{\pi }{2}\times 0.5)=\sqrt{2}\pi cm$