$A$ source of sound $S$ having frequency $f$. Wind is blowing from source to observer $O$ with velocity $u$. If the speed of sound with respect to air is $C$,the wavelength of sound detected by $O$ is:

An earthquake generates both transverse $S$ and longitudinal $P$ waves in the earth with speeds $4.5 \,km/s$ and $8.0 \,km/s$, respectively. $A$ seismograph records that the first $P$-wave arrives $3.5 \,min$ earlier than the first $S$-wave. From the seismograph, the epicentre of the earthquake is located at a distance of: (in $\,km$)

Consider the sound wave travelling in ideal gases of $He$,$CH_4$,and $CO_2$. All the gases have the same ratio $\frac{P}{\rho}$,where $P$ is the pressure and $\rho$ is the density. The ratio of the speed of sound through the gases $V_{He}: V_{CH_4}: V_{CO_2}$ is given by

$A$ train,standing in a station yard,blows a whistle of frequency $400 \, Hz$ in still air. The wind starts blowing in the direction from the yard to the station with a speed of $10 \, m/s$. Given that the speed of sound in still air is $340 \, m/s$. Mark the $INCORRECT$ statement:

The particle displacement of a travelling longitudinal wave is represented by $\xi = \xi(x, t)$. The midpoints of a compression zone and an adjacent rarefaction zone are represented by the letters $C$ and $R$. Which of the following is true?

The pressure wave,$P = 0.01 \sin(1000t - 3x) \, N m^{-2}$,corresponds to the sound produced by a vibrating blade on a day when atmospheric temperature is $0 \, ^oC$. On some other day when temperature is $T$,the speed of sound produced by the same blade and at the same frequency is found to be $336 \, m s^{-1}$. The approximate value of $T$ is .... $^oC$