Question 11:
moderate
In the given progressive wave equation y = 0.5 sin (10πt – 5x); where x, y in cm and t in second. The maximum velocity of the particle is
Question 12:
moderate
The path difference between the two waves
\[ y_{1}= a_{1} sin \left( \omega t -\frac{2\Pi x}{\lambda} \right) \]
and
\[ y_{2}= a_{2} cos \left( \omega t -\frac{2\Pi x}{\lambda} + \varphi \right) \]
is
Question 13:
moderate
The \(4^{\text{th}}\) overtone of a closed organ pipe is same as that of \(3^{\text{th}}\) overtone of an open pipe. The ratio of the length of the closed pipe to the length of the open pipe is:
The frequency of the \(4^{\text{th}}\) overtone (9th harmonic) of a closed pipe is \(f_c = \frac{9v}{4L_c}\). The frequency of the \(3^{\text{rd}}\) overtone (4th harmonic) of an open pipe is \(f_o = \frac{4v}{2L_o} = \frac{2v}{L_o}\). Equating the two, \(\frac{9v}{4L_c} = \frac{2v}{L_o} ⇒ \frac{L_c}{L_o} = \frac{9}{8}\).