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

The amplitude of a wave represented by displacement equation $y = \frac{1}{{\sqrt a }}\,\sin \,\omega t \pm \frac{1}{{\sqrt b }}\,\cos \,\omega t$ will be

The apparent frequency of a sound wave as heard by an observer is $10\%$ more than the actual frequency. If the velocity of sound in air is $330\, m/sec$, then 
$(i)$ The source may be moving towards the observer with a velocity of $30\,ms^{-1}$
$(ii)$ The source may be moving towards the observer with a velocity of $33\,ms^{-1}$
$(iii)$ The observer may be moving towards the source with a velocity of $30\,ms^{-1}$
$(iv)$ The observer may be moving towards the source with a velocity of $33\,ms^{-1}$

During propagation of a plane progressive mechanical wave incorrect statement is

The equation of a stationary wave is

$y = 0.8\,\cos \,\,\left( {\frac{{\pi x}}{{20}}} \right)\,\sin \,200\,\pi t$

where $x$ is in $cm$ and $t$ is in $sec$ . The separtion between consecutive nodes will be .... $cm$

A stretched wire of length $110\,cm$ is divided into three segments whose frequencies are in ratio $1 : 2 : 3.$ Their lengths must be