Two sources of sound placed close to each other are emitting progressive waves given by ${\mathrm{y}}_1=4\sin 600\mathrm{\pi t}$ and ${\mathrm{y}}_2=5\sin 608\mathrm{\pi t}.$ An observer located near these two sources of sound will hear:

A source of unknown frequency gives $4 \mathrm{beats} {\mathrm{s}}^{-1}$, when sounded with a source of known frequency $250 \mathrm{Hz}$. The second harmonic of the source of unknown frequency gives $\mathrm{five} \mathrm{beats} \mathrm{per} \mathrm{second}$, when sounded with a source of frequency $513 \mathrm{Hz}$. The unknown frequency is 

If we study the vibration of a pipe open at both ends, then which of the following statements is not true?

The fundamental frequency of a closed organ pipe of length $20 \mathrm{cm}$ is equal to the second overtone of an organ pipe open at both the ends. The length of organ pipe open at both the ends is

An air column, closed at one end and open at the other, resonates with a tuning fork when the smallest length of the column is $50 \mathrm{cm}$. The next larger length of the column resonating with the same tuning fork is