A stretched wire of length $110\,cm$ is divided into three segments whose frequencies are in ratio $1 : 2 : 3.$ Their lengths must be

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   .... $Hz$

The equation of transverse wave in stretched string is $y = 5\,\sin \,2\pi \left[ {\frac{t}{{0.04}} - \frac{x}{{50}}} \right]$ Where distances are in cm and time in second. The wavelength of wave is .... $cm$

Two tuning forks $A$ and $B$ produce $8\, beats/s$ when sounded together. $A$ gas column $37.5\, cm$ long in a pipe closed at one end resonate to its fundamental mode  with fork $A$ whereas a column of length $38.5 \, cm$ of the same gas in a similar pipe  is required for resonance with fork $B$. The frequencies of these two tuning forks, are

Calculate the temperature at which the speed of sound will be two times its   ..... $K$ value at $0\,^oC$

Two tuning forks $A$ and $B$ produce $8\,beats/s$ when sounded together. $A$ gas column $37.5\,cm$ long in a pipe closed at one end resonate to its fundamental mode with fork $A$ whereas a column of length $38.5\,cm$ of the same gas in a similar pipe is required for resonance with fork $B$. The frequencies of these two tuning forks, are