The fundamental frequency of transverse wave of a stretched string subjected to a tension $T_1$ is 300 Hz . If the length of the string is doubled and subjected to a tension of $T_2$, the fundamental frequency of the transverse wave in the string becomes 100 Hz , then $T_2: T_1=$

(Linear density of the string is constant)

Two sound waves each of intensity $I$ are superimposed. If the phase difference between the waves is $\frac{\pi}{2}$, then the intensity of the resultant wave is

Two closed pipes when sounded simultaneously in their fundamental modes produce 6 beats per second. If the length of the shorter pipe is 150 cm , then the length of the longer pipe is

(Speed of sound in air $=336 \mathrm{~ms}^{-1}$ )