A wave travelling along the $x-$ axis is described by the equation $y \,(x, t ) = 0.005\, cos \,\left( {\alpha x – \beta t} \right)$. If the wavelength and the time period of the wave are $0.08\,m$ and $2.0\, s$ respectively then $a$ and $b$ in appropriate units are

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

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 ….. $Hz$

A point source emits sound equally in all directions in a non-absorbing medium. Two points $P$ and $Q$ are at a distance of $9$ meters and $25$ meters respectively from the source. The ratio of the amplitudes of the waves at $P$ and $Q$ is

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 ….. $Hz$