A) 3 cm
B) 4.5 cm
C) 6 cm
D) 1.5 cm
Correct Answer: D
Solution :
The nodes and antinodes are formed in a standing wave pattern as a result of the interference of two waves. Distance between two nodes is half of wavelength\[(\lambda )\] standard equation of standing wave is \[y=2a\sin \frac{2\pi x}{\lambda }\cos \frac{2\pi vt}{\lambda }\] ...(i) where a is amplitude,\[\lambda \]the wavelength, v the velocity and t the time. Given, equation is \[y=5\sin \frac{2\pi x}{3}\cos 20\pi t\] ...(ii) Comparing Eqs. (ii) with (i), we have \[\frac{2\pi x}{\lambda }=\frac{2\pi x}{3}\] \[\Rightarrow \] \[\lambda =3\,cm\] Hence, distance between two adjacent nodes is\[\frac{\lambda }{2}\]. \[=\frac{3}{2}=1.5\,cm\] Note: Standing wave is not actually a wave but rather a pattern which results from the interference of two or more waves. Since, standing wave is not technically a wave, then an antinode is not technically a point on a wave. The nodes and antinodes are merely points on the medium which up the wave pattern.You need to login to perform this action.
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