$y = a\,cos\,(kx -\omega t)$ superposes on another wave giving a stationary wave having node at $x = 0$ . What is the equation of the other wave 

A train whistling at constant frequency is moving towards a station at a constant speed $v$. The train goes past a stationary observer on the station. The frequency $n$ of the sound as heard by the observer is plotted as a function of time $t$. Identify the expected curve

A point source emits sound equally in all directions in a non-absorbing medium. Two points $P$ and $Q$are at distances of $2m$ and $3m$ respectively from the source. The ratio of the intensities of the waves at $P$ and $Q$ is

A train whistling at constant frequency is moving towards a station at a constant speed $V$. The train goes past a stationary observer on the station. The frequency $n'$ of the sound as heard by the observer is plotted as a function of time $t (Fig.)$ . Identify the expected curve

A string of mass $M$ and length $L$ hangs freely from a fixed point. The velocity of transverse wave along the string at a distance $'x'$ from the free end will be

 Two cars $A$ and $B$ are moving in the same direction with speeds $36\,km/hr$ and $54\,km/hr$ respectively. Car $B$ is ahead of $A$. If $A$ sounds horn of frequency $1000\,Hz$ and the speed of sound in air is $340\,m/s$, the frequency of sound received by the driver of car $B$ is .................. $\mathrm{Hz}$