The frequency of the sound produced by a siren increases from$400 \mathrm{Hz} \mathrm{to} 1200 \mathrm{Hz}$while its amplitude remains the same. Therefore, the ratio of the intensity of the $1200 \mathrm{Hz}$ wave to that of the $400 \mathrm{Hz}$wave is 

The two pipes are submerged in seawater, arranged as shown in the figure. Pipe $A$ with length $L_{\mathrm{A}} = 1.5 \mathrm{m}$and one open end contains a small sound source that sets up the standing wave with the second-lowest resonant frequency of that pipe. Sound from pipe $A$ sets up a resonance in pipe $B$, which has both ends open. The resonance is at the second lowest resonant frequency of pipe $B.$ The length of the pipe $B$ in meters is : 

Two narrow cylindrical pipes $A$ and $B$ have the same length. The pipe $A$ is open at both ends and is filled with a monoatomic gas of molar mass $M_{\mathrm{A}}$. The pipe $B$ is open at one end and closed at the other end and is filled with a diatomic gas of molar mass $M_{\mathrm{B}}$. Both gases are at the same temperature.

$\left(\mathrm{a}\right)$ If the frequency of the second harmonic of the fundamental mode in the pipe $A$ is equal to the frequency of the third harmonic of the fundamental mode in the pipe $B$, determine the value of $\frac{M_{\mathrm{A}}}{M_{\mathrm{B}}}$.
$\left(\mathrm{b}\right)$ Now, the open end of the pipe $B$ is also closed (so that the pipe is closed at both ends). Find the ratio of the fundamental frequency in the pipe $A$ to that in the pipe $B$.