In an organ pipe closed at one end,the sum of the frequencies of the first three overtones is $3930 \ Hz$. The frequency of the fundamental mode of the organ pipe is: (in $Hz$)

Consider a gas with molar mass $M$. If sound at frequency $f$ is introduced to a tube of this gas at temperature $T$, an internal acoustic standing wave is set up with nodes separated by $L$. The adiabatic constant $\gamma = \frac{C_p}{C_v}$ is

Consider the following statements about stationary waves:
$A$. The distance between two adjacent nodes or antinodes is equal to $\frac{\lambda}{2}$ $(\lambda = \text{wavelength of the wave})$.
$B$. $A$ pressure node is always formed at the open end of the open organ pipe.
Choose the correct option from the following:

If we study the vibration of a pipe open at both ends,then the following statement is not true.

$A$ 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 $\,Hz$)

An open pipe of length $L_1$ has a fundamental frequency $n_1$,and a closed pipe of length $L_2$ has a fundamental frequency $n_2$. If they are joined to form a single closed pipe of length $L = L_1 + L_2$,what is the fundamental frequency of the combined pipe?