question_answer 42)

                  The transverse displacement of a string (clamped at its both ends) is given by \[y\,(x,\,t)=0.06\]\[\sin \,(2\pi x/3)\,\cos \,(120\,\pi t)\]. All the points on the string between two consecutive nodes vibrate with                 (a) same frequency                        (b) same phase                 (c) same energy                                               (d) different amplitude.

Answer:

                  (a, b, c) \[y\,(x,\,t)=0.06\,\sin \left( \frac{2\pi x}{3} \right)\cos \,(120\,\pi t)\].                 It is the equation of a stationary wave.