An engine is moving towards a wall with a velocity $50\, ms^{-1}$ emits a note of $1.2\, kHz$. The speed of sound in air is $350\, ms^{-1}$. The frequency of the note after reflection from the wall as heard by the driver of the engine is ..... $kHz$

A metallic wire of length $L$ is fixed between two rigid supports. If the wire is cooled through a temperature difference $\Delta T (Y =$ young’s modulus, $\rho =$ density, $\alpha =$ coefficient of linear expansion) then the frequency of transverse vibration is proportional to : 

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

A uniform rope of length $L$ and mass $m_1$ hangs vertically from a rigid support. A block of mass $m_2$ is attached to the free end of the rope. A transverse pulse of wavelength $\lambda _1$ is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is $\lambda _2$. The ratio $\lambda _2/\lambda _1$ 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   .... $Hz$

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