Two identical flutes produce fundamental notes of frequency $300 \ Hz$ at $27 \ ^oC$. If the temperature of air in one flute is increased to $31 \ ^oC$,the number of beats heard per second will be

$A$ stretched uniform wire of length $L$ under tension $T$ is vibrating with fundamental frequency $n$. $A$ closed pipe of the same length $L$ is also vibrating with the same fundamental frequency $n$. If the tension $T$ is increased by $16 \,N$, the wire resonates with the $2^{\text{nd}}$ harmonic of the same closed pipe. The initial tension in the wire is: (in $\,N$)

The length,tension,diameter,and density of a wire $B$ are double those of the corresponding quantities for another stretched wire $A$. Then:

Speed of a transverse wave on a straight wire (mass $6.0\; g$,length $60\; cm$,and area of cross-section $1.0\; mm^{2}$) is $90\; ms^{-1}$. If the Young's modulus of the wire is $16 \times 10^{11}\; Nm^{-2}$,the extension of the wire over its natural length is: (in $; mm$)

$A$ pipe closed at one end has a length of $0.8 \ m$. At its open end,a $0.5 \ m$ long uniform string is vibrating in its second harmonic and it resonates with the fundamental frequency of the pipe. If the tension in the wire is $50 \ N$ and the speed of sound is $320 \ m/s$,the mass of the string is: (in $g$)