$Assertion :$ The pitch of wind instruments rises and that of string instruments falls as an orchestra warms up.
$Reason :$ When temperature rises,the speed of sound increases,but the speed of a wave in a string fixed at both ends decreases.

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

$A$ wave is travelling along a string. At an instant,the shape of the string is as shown in the figure. At this instant,point $A$ is moving upward. Then:
$(a)$ The wave is travelling to the left.
$(b)$ At this instant,$C$ is moving downward.
$(c)$ The amplitude of the wave is greater than the displacement of point $B$ at this instant.
$(d)$ The phase at $A$ is less than the phase at $C$.
Select the correct statements:

$A$ wave equation is given as $y = \cos(500t - 70x)$,where $y$ is in $mm$,$x$ is in $m$,and $t$ is in $s$. Which of the following statements is correct?

$A$ narrow tube is bent in the form of a circle of radius $R,$ as shown in the figure. Two small holes $S$ and $D$ are made in the tube at positions right-angled to each other. $A$ source placed at $S$ generates a wave of intensity $I_0$ which is equally divided into two parts: one part travels along the longer path,while the other travels along the shorter path. Both the waves meet at point $D$ where a detector is placed. If a maxima is formed at the detector,then the possible values for the wavelength $\lambda$ of the wave produced are given by:

$A$ transverse sinusoidal wave of amplitude $a,$ wavelength $\lambda,$ and frequency $n$ is travelling on a stretched string. The maximum speed of any point on the string is $v/10,$ where $v$ is the speed of propagation of the wave. If $a = 10^{-3} \ m$ and $v = 10 \ m/s,$ then $\lambda$ and $n$ are given by: