An organ pipe $P_1$ closed at one end vibrating in its first overtone. Another pipe $P_2$  open at both ends is vibrating in its third overtone. They are in a resonance with a  given tuning fork. The ratio of the length of $P_1$ to that of $P_2$ is

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?

For a certain organ pipe three successive resonance frequencies are observed at $425\, Hz,595 \,Hz$ and $765 \,Hz$ respectively. If the speed of sound in air is $340 \,m/s$,  then the length of the pipe is ..... $m$

Dependence of disturbances due to two waves on time is shown in the figure. The ratio of their intensities $I_1 / I_2$ will be

Equation of a plane progressive wave is given by $y = 0.6\sin 2\pi \left( {t - \frac{x}{2}} \right)$. On reflection from a denser medium its amplitude becomes $2/3$ of the amplitude of the incident wave. The equation of the reflected wave is

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 $33\,ms^{-1}$