A railway engine whistling at a constant frequency moves with a constant speed. It goes past a stationary observer standing beside the  railway track. The frequency $(n)$ of the sound heard by the observer is plotted against time $(t).$ Which of the following best represents the resulting curve?

A train is moving towards a stationary observer. Which of the following curve best represents the frequency received by observer $f$ as a function of time ?

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 monoatomic ideal gases $1$ and $2$ of molecular masses $M_1$ and $M_2$ respectively are enclosed in separate containers kept a the same temperature. The ratio of the speed of sound in gas $1$ to that in gas $2$ is

When two waves of almost equal frequencies $v_1$ and $v_2$ reach at a point simultaneously, the time interval between successive maxima is

A sound-source is moving in a circle and an observer is outside the circle at $O$ as shown in figure. If the frequencies as heard by the listener are $\nu _1, \nu _2$ and $\nu _3$ when the source is at $A, B$ and $C$ position, respectively, then