Why are the speeds of longitudinal and transverse waves in a solid different? Explain.

If the pressure,temperature,and density of an ideal gas are denoted by $p, T$ and $\rho$,respectively,the velocity of sound in the gas is

$A$ source $S$ of frequency $f_0$ and an observer $O$,moving with speeds $v_1$ and $v_2$ respectively,are moving away from each other. When they are separated by a distance $a$ at $t = 0$,a pulse is emitted by the source. This pulse is received by $O$ at time $t_1$. Then $t_1$ is equal to:

$A$ plane wave of sound traveling in air is incident upon a plane surface of a liquid. The angle of incidence is $60^{\circ}.$ The speed of sound in air is $300 \, m/s$ and in the liquid it is $600 \, m/s.$ Assume Snell's law to be valid for sound waves.

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

The ratio of the velocity of sound in hydrogen $\left(\gamma=\frac{7}{5}\right)$ to that in helium $\left(\gamma=\frac{5}{3}\right)$ at the same temperature is