The frequency of a stretched uniform wire of length $L$ under tension is in resonance with the fundamental frequency of a closed pipe of same length. If the tension in the wire is increased by 8 N , it is in resonance with the first overtone of the same closed pipe. The initial tension in the wire is

When an observer moves towards a stationary source with velocity ' $\mathrm{V}_1$ ', the apparent frequency of emitted note is ' $\mathrm{F}_1$ '. When observer moves away from stationary source with velocity ' $\mathrm{V}_1$ ' the apparent frequency is ' $\mathrm{F}_2$ '. If ' v ' is velocity of sound in air and $\frac{\mathrm{F}_1}{\mathrm{~F}_2}=2$, then $\frac{\mathrm{V}}{\mathrm{V}_1}$ is equal to

In fundamental mode, the time required for the sound wave to reach up to closed end of a pipe filled with air is ' $t$ ' second. The frequency of vibration of air column is (Neglect end correction)

Two pipes of lengths $\mathrm{L}_1$ and $\mathrm{L}_2$, open at both ends are joined in series. If ' $f_1$ ' and ' $f_2$ ' are the fundamental frequencies of two pipes, then the fundamental frequency of series combination will be (neglect end correction)