question_answer

The equation of stationary wave is\[y=0.8\cos \left( \frac{\pi x}{20} \right)\sin 200\pi t\] where x is in cm and t is in sec. The separation between two consecutive nodes will be :

A)  5 cm                                     

B)  1.5 cm

C)  10 cm                                  

D)  20 cm

Correct Answer: D

Solution :

                                                                                   Here, the equation is \[y=0.8\cos \frac{\pi x}{20}\sin 200\pi t\]       ?...(i) Now, the standard equation of stationary wave is \[y=a\cos \frac{2\pi x}{\lambda }\sin \omega t\]           ??(ii) Now, comparing the given equation (i) with standard equation (ii) we obtain \[\frac{2\pi }{\lambda }=\frac{\pi }{20}\] So,      \[\lambda =40cm\] Hence, distance between consecutive node is \[=\frac{\lambda }{2}=\frac{40}{2}=20cm\]