Equation of simple harmonic progressive wave is given by $$y=\frac{1}{\sqrt{a}} \sin \omega t \pm \frac{1}{\sqrt{b}} \cos \omega t$$ then the resultant amplitude of the wave is $$\left(\cos 90^{\circ}=0\right)$$

When a string of length '$$l$$' is divided into three segments of length $$l_1, l_2$$ and $$l_3$$. The fundamental frequencies of three segments are $$\mathrm{n}_1, \mathrm{n}_2$$ and $$\mathrm{n}_3$$ respectively. The original fundamental frequency '$$n$$' of the string is

A closed organ pipe of length '$$L_1$$' and an open organ pipe contain diatomic gases of densities '$$\rho_1$$' and '$$\rho_2$$' respectively. The compressibilities of the gases are same in both pipes, which are vibrating in their first overtone with same frequency. The length of the open organ pipe is (Neglect end correction)

A stationary wave is represented by $$\mathrm{y}=10 \sin \left(\frac{\pi \mathrm{x}}{4}\right) \cos (20 \pi \mathrm{t})$$ where $$\mathrm{x}$$ and $$\mathrm{y}$$ are in $$\mathrm{cm}$$ and $$\mathrm{t}$$ in second. The distance between two consecutive nodes is