A car $P$ approaching a crossing at a speed of $10\, m/s$ sounds a horn of frequency $700\, Hz$ when $40\, m$ in front of the crossing. Speed of sound in air is $340\, m/s$. Another car $Q$ is at rest on a road which is perpendicular to the road on which car $P$ is reaching the crossing (see figure). The driver of car $Q$ hears the sound of the horn of car $P$ when he is $30\, m$ in front of the crossing. The apparent frequency heard by the driver of car $Q$ is …… $Hz$

If $L_1$ and $L_2$ are the lengths of the first and second resonating air columns in a resonance tube, then the wavelength of the note produced is

Two trains $A$ and $B$ initially $120\, km$ apart, start moving towards each other on the same track with a velocity of $60\, km/hr$ each. At the moment of start $A$ blows a whistle, which reflects on $B$ and subsequently reflects from $A$ and so on. Take the velocity of sound waves in air $1200\, km/hr$. The distance travelled by sound waves before the trains crash will be (in $km$)

Two vibrating tuning forks produce waves given by ${y_1} = 4\sin 500\pi t$ and ${y_2} = 2\sin 506\pi t.$  Number of beats produced per minute is

A closed organ pipe has a frequency $'n'$. If its length is doubled and radius is halved, its frequency nearly becomes