Derivation of the Speed of Sound

Q.

In a liquid with density $1300\frac{kg}{m^3}$, longitudinal waves with frequency 400 Hz are found to have wavelength 8.00 m. Calculate the bulk modulus of the liquid.

1. $1.33\times {10}^{10}\frac{N}{m^2}$

2. $3.33\frac{N}{m^2}$

3. $3.33\times {10}^{10}\frac{N}{m^2}$

4. $1.33\frac{N}{m^2}$

Q. The displacement of a particle of the medium due to a wave moving in the positive $x-$ direction is given by $y=\frac{1}{(1+x^2)}$ at time $t=0$ and by $y=\frac{1}{1+{(x-1)}^2}$ at $t=2$ second, where $x$ and $y$ are in metre. The velocity of the wave in $\text{m/s}$ is

1. $0.5$

2. $1$

3. $2$

4. $4$

Q. Determine the change in volume of $6\text{litres}$ of alcohol if the pressure is decreased from $200\text{cm}$ of $Hg$ to $75\text{cm}$ of $Hg$.
[Velocity of sound in alcohol is $1280\text{m/s}$ density of alcohol $=0.81\text{gm/cc}$, density of $Hg=13.6\text{gm/cc}$ and $g=981{\text{cm/s}}^2$]

1. $0.5\text{mL}$
2. $0.75\text{mL}$
3. $1\text{mL}$
4. $2\text{mL}$

Q. Find the speed of sound in $H_2$ gas if the speed of sound in $O_2$ gas is $450\text{m/s}$ at the same temperature.

1. $1800\text{m/s}$
2. $1200\text{m/s}$
3. $1500\text{m/s}$
4. $1600\text{m/s}$