Explain the reflection of wave at free support.

Two open organ pipes of fundamental frequencies $n_{1}$ and $n_{2}$ are joined in series. The fundamental frequecny of the new pipe so obtained will be

A string on a musical instrument is $50 cm$ long and its fundamental frequency is $270 Hz$. If the desired frequency of $1000 Hz$ is to be produced, the required length of the string is .... $cm$

The pattern of standing waves formed on a stretched string at two instants of time are shown in figure. The velocity of two waves superimposing to form stationary waves is $360$ $\mathrm{ms}^{-1}$ and their frequencies are $256$ $\mathrm{Hz}$.

$(a)$ Calculate the time at which the second curve is plotted.

$(b)$ Mark nodes and antinodes on the curve.

$(c)$ Calculate the distance between $\mathrm{A}^{\prime}$ and $\mathrm{C}^{\prime}$.

A vibrating string of certain length $\ell$ under a tension $\mathrm{T}$ resonates with a mode corresponding to the first overtone (third harmonic) of an air column of length $75 \mathrm{~cm}$ inside a tube closed at one end. The string also generates $4$ beats per second when excited along with a tuning fork of frequency $\mathrm{n}$. Now when the tension of the string is slightly increased the number of beats reduces $2$ per second. Assuming the velocity of sound in air to be $340 \mathrm{~m} / \mathrm{s}$, the frequency $\mathrm{n}$ of the tuning fork in $\mathrm{Hz}$ is

In Melde's experiment, the string vibrates in $4$ loops when a $50 \,gram$ weight is placed in the pan of weight $15\, gram.$ To make the string to vibrates in $6$ loops the weight that has to be removed from the pan is