A sound wave of frequency $\nu$ travels horizontally to the right. It is reflected from a large vertical plane surface, moving to the left with a speed $v$. If the speed of sound in the medium is $c$, then study the following statements.

A detector is released from rest over height h a source of sound of frequency $f_0={10}^3\mathrm{Hz}$. The frequency observed by the detector at time$t$  is plotted in the graph. The speed of sound in air is $\left(g=10 \mathrm{m} {\mathrm{s}}^{-2}\right)$

Four open organ pipes of different lengths and different gases at same temperature as shown in figure. Let ${\mathrm{f}}_{\mathrm{A}}, {\mathrm{f}}_{\mathrm{B}}, {\mathrm{f}}_{\mathrm{C}}$ and ${\mathrm{f}}_{\mathrm{D}}$ be their fundamental frequencies then : [Take ${\mathrm{\gamma }}_{{\mathrm{CO}}_2}=7/5$]

In an organ pipe whose one end is at $x=0$, the pressure is expressed by $P=P_{0} \cos \frac{3 \pi x}{2} \sin 300 \pi t$ where $x$ is in metre and $t$ in seconds. The organ pipe can be

The vibrations of a string of length $60 \mathrm{cm}$ fixed at both ends are represented by the equation :$y=4\sin \left(\frac{\pi x}{15}\right)\cos \left(96\pi t\right)$ where $x$ and $y$ are in $\mathrm{cm}$ and$t$ in seconds.

What is the maximum displacement in $\left(\mathrm{cm}\right)$ of a point at $x=5 \mathrm{cm}$ ?