A sound-source is moving in a circle and an observer is outside the circle at $O$ as shown in figure. If the frequencies as heard by the listener are $\nu _1, \nu _2$ and $\nu _3$ when the source is at $A, B$ and $C$ position, respectively, then

The transverse displacement of a string (clamped at its both ends) is given by $y(x,t) = 0.06$ $sin\, (2\pi x /3)\, cos\, (120\, \pi t)$. All the points on the string between two consecutive nodes vibrate with

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 in $0.08\ m$ and $2.0\ s$ respectively then $\alpha $ and $\beta $ in appropriate units are

Two pipes are each $50\,cm$ in length. One of them is closed at one end while the other is  both ends. The speed of sound in air is $340\,ms^{-1}.$ The frequency at which both the pipes can resonate is