A cylindrical tube open at both ends has a fundamental frequency $f$ in air. The tube is dipped vertically in water, so that half of it is in water. The new fundamental frequency is

Which of the following wave has the largest wave speed?

A wire of length 0.4 m stretched at both ends vibrates 250 times per second. If the length of the wire is increased by 0.1 m and the stretching force is reduced to $1 / 4$ th of its original value, then the new frequency is

Two strings $A$ and $B$ produce beat of frequency $\Delta f_1>0$. The tension in string $A$ is slightly increased and the beat frequency is found to be $\Delta f_2>0$. If the original frequency of $A$ is $f_0$ and $\Delta f_2<\Delta f_1$, then the frequency of $B$ is