The lengths of the two organ pipes open at both ends are $L$ and $(L+L_1)$. If they are sounded together,the beat frequency will be ($v=$ velocity of sound in air).

$A$ tuning fork of frequency $500 \ Hz$ is sounded on a resonance tube. The first and second resonance are obtained at $17 \ cm$ and $52 \ cm$. The velocity of sound is $........ \ m/s$.

$A$ closed pipe is suddenly opened and changed to an open pipe of the same length. The fundamental frequency of the resulting open pipe is less than that of the $3^{rd}$ harmonic of the earlier closed pipe by $55 \,Hz$. Then, the value of the fundamental frequency of the closed pipe is: (in $\,Hz$)

$A$ standing wave in a pipe with a length $L=1.2 \,m$ is described by $y(x, t)=y_0 \sin [(2 \pi / L) x] \sin [(2 \pi / L) x+\pi / 4]$. Based on the above information,which one of the following statements is incorrect? (Speed of sound in air is $300 \,ms^{-1}$)

Two open organ pipes of length $25 \ cm$ and $25.5 \ cm$ produce $10 \ \text{beats/sec}$. The velocity of sound will be ..... $m/s$.

$A$ tuning fork with frequency $800 \; Hz$ produces resonance in a resonance column tube with the upper end open and the lower end closed by a water surface. Successive resonances are observed at lengths $9.75 \; cm$,$31.25 \; cm$,and $52.75 \; cm$. The speed of sound in air is ...... $m/s$.