In a standing wave on a string.

Two persons $A$ and $B$, each carrying a source of frequency $596 \mathrm{Hz}$ and $600 \mathrm{Hz}$, respectively, are standing at rest, a few $\mathrm{metres}$ apart. $A$ starts moving towards $B$ with a velocity of $2 \mathrm{m} {\mathrm{s}}^{-1}$. If the speed of sound is $300 \mathrm{m} {\mathrm{s}}^{-1}$, which of the following statement is true?

A $20 \mathrm{cm}$ long string, having a mass of $1.0 \mathrm{g}$, is fixed at both ends. The tension in the string is $0.5 \mathrm{N}$. The string is set into vibration using an external vibrator of frequency $100 \mathrm{Hz}$. Find the separation (in $\mathrm{cm}$) between the successive nodes on the string.

The figure shows a string of linear mass density $1.0 \mathrm{g} {\mathrm{cm}}^{-1}$ on which a wave pulse is travelling. Find the time taken (in $\mathrm{mS}$) by the pulse in travelling through a distance of $60 \mathrm{cm}$ on the string. Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$.

If two closed organ pipes of $750 \mathrm{cm}, 770 \mathrm{cm}$ length are sounded together in the fundamental mode, then $3$ beats per second are produced. Based on this observation, find the velocity of sound in $\mathrm{m} {\mathrm{s}}^{-1}$: