Q: Which type of mechanical waves can propagate inside liquids and gases?

Correct Option: Only Longitudinal waves \nLongitudinal waves can propagate through solids, liquids, and gases because all these states of matter possess bulk modulus of elasticity. Transverse mechanical waves require shear modulus, which liquids and gases lack.

Q: According to Laplace's correction, the speed of sound in an ideal gas is given by which formula?

Correct Option: $v = \sqrt{\frac{\gamma P}{\rho}}$ \nLaplace corrected Newton's formula by assuming that sound propagation in a gas is an adiabatic process, giving $v = \sqrt{\frac{\gamma P}{\rho}}$, where $\gamma$ is the ratio of specific heats.

Q: What is the distance between two consecutive nodes in a stationary wave?

Correct Option: $\lambda / 2$ \nIn a stationary wave, the distance between any two consecutive nodes (or two consecutive antinodes) is equal to half of the wavelength, which is $\frac{\lambda}{2}$.

Q: When two sound waves of slightly different frequencies $f1$ and $f2$ superimpose, the beat frequency produced per second is:

Correct Option: $|f1 - f2|$ \nBeat frequency is the absolute difference between the frequencies of two superimposing sound waves, given by $f{beat} = |f1 - f2|$.

Q: What is the ratio of fundamental frequencies of a closed organ pipe and an open organ pipe of the same length?

Correct Option: $1 : 2$ \nFundamental frequency of closed pipe $fc = \frac{v}{4L}$ and open pipe $fo = \frac{v}{2L}$.\nRatio $\frac{fc}{fo} = \frac{v/4L}{v/2L} = \frac{1}{2}$, i.e., $1:2$.

Question 1

Which type of mechanical waves can propagate inside liquids and gases?

Accepted Answer

Correct Option: Only Longitudinal waves 
Longitudinal waves can propagate through solids, liquids, and gases because all these states of matter possess bulk modulus of elasticity. Transverse mechanical waves require shear modulus, which liquids and gases lack.

Question 2

According to Laplace's correction, the speed of sound in an ideal gas is given by which formula?

Accepted Answer

Correct Option: $v = \sqrt{\frac{\gamma P}{ho}}$ 
Laplace corrected Newton's formula by assuming that sound propagation in a gas is an adiabatic process, giving $v = \sqrt{\frac{\gamma P}{ho}}$, where $\gamma$ is the ratio of specific heats.

Question 3

What is the distance between two consecutive nodes in a stationary wave?

Accepted Answer

Correct Option: $\lambda / 2$ 
In a stationary wave, the distance between any two consecutive nodes (or two consecutive antinodes) is equal to half of the wavelength, which is $\frac{\lambda}{2}$.

Question 4

When two sound waves of slightly different frequencies $f1$ and $f2$ superimpose, the beat frequency produced per second is:

Accepted Answer

Correct Option: $|f1 - f2|$ 
Beat frequency is the absolute difference between the frequencies of two superimposing sound waves, given by $f{beat} = |f1 - f2|$.

Question 5

What is the ratio of fundamental frequencies of a closed organ pipe and an open organ pipe of the same length?

Accepted Answer

Correct Option: $1 : 2$ 
Fundamental frequency of closed pipe $fc = \frac{v}{4L}$ and open pipe $fo = \frac{v}{2L}$.
Ratio $\frac{fc}{fo} = \frac{v/4L}{v/2L} = \frac{1}{2}$, i.e., $1:2$.

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