A closed organ and an open organ tube are filled by two different gases having same bulk modulus but different densities $\rho_1$ and $\rho_2$, respectively. The frequency of $9^{\text {th }}$ harmonic of closed tube is identical with $4^{\text {th }}$ harmonic of open tube. If the length of the closed tube is 10 cm and the density ratio of the gases is $\rho_1: \rho_2=1: 16$, then the length of the open tube is :

A plane progressive wave is given by $$y=2 \cos 2 \pi(330 \mathrm{t}-x) \mathrm{m}$$. The frequency of the wave is :

The fundamental frequency of a closed organ pipe is equal to the first overtone frequency of an open organ pipe. If length of the open pipe is $$60 \mathrm{~cm}$$, the length of the closed pipe will be:

A car P travelling at $$20 \mathrm{~ms}^{-1}$$ sounds its horn at a frequency of $$400 \mathrm{~Hz}$$. Another car $$\mathrm{Q}$$ is travelling behind the first car in the same direction with a velocity $$40 \mathrm{~ms}^{-1}$$. The frequency heard by the passenger of the car $$\mathrm{Q}$$ is approximately [Take, velocity of sound $$=360 \mathrm{~ms}^{-1}$$ ]