Two superimposing waves are represented by the equations $y_1 = 2 \sin 2 \pi(10 t - 0.4 x)$ and $y_2 = 4 \sin 2 \pi(20 t - 0.8 x)$. The ratio of $I_{\max}$ to $I_{\min}$ is ........

$Assertion :$ 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.

$A$ wave pulse on a string has the dimensions shown in the figure. The wave speed is $v = 1 \, cm/s$. If point $O$ is a free end,what is the shape of the wave at time $t = 3 \, s$?

An object of density $2000 \ kg \ m^{-3}$ is hung from a thin light wire. The fundamental frequency of the transverse waves in the wire is $200 \ Hz$. If the object is immersed in water such that half of its volume is submerged,then the fundamental frequency of the transverse waves in the wire is (in $Hz$)

$A$ composite string is made up by joining two strings of different masses per unit length $\mu$ and $4\mu$. The composite string is under the same tension. $A$ transverse wave pulse $Y = (6 \text{ mm}) \sin(5t + 40x)$,where $t$ is in seconds and $x$ in meters,is sent along the lighter string towards the joint. The percentage of power transmitted to the heavier string through the joint is approximately ..... $\%$

In Quincke's tube,a detector detects minimum intensity. Now,one of the tubes is displaced by $5 \, cm$. During displacement,the detector detects maximum intensity $10$ times,and finally a minimum intensity (when displacement is complete). The wavelength of sound is .... $cm$.