A set of $24$ tunning fork is arranged in a series of increasing frequencies. If each fork gives $4\, beats/second$ with the preceeding one and frequency of last tunning fork is two times of first fork. Find frequency of $5^{th}$ tunning fork  .... $Hz$

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 vibrating strings of the same material but lengths $L$ and $2L$ have radii $2r$ and $r$ respectively. They are stretched under the same tension . Both the strings vibrate in their fundamental modes, the one of length $L$ with frequency $f_1$ and the other with frequency $f_2$. The ratio $\frac{f_1}{f_2}$ is given by

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

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 string of mass $2.5\ kg$ is under a tension of $200\ N$ . The length of the stretched string is $20.0\ m$ . If the transverse jerk is struck at one end of the string, the disturbance will reach the other end in .... $\sec$