Pressure Wave vs Displacement Wave

Q. If the pressure amplitude of sound wave in a medium is tripled and the wavelength is doubled then the amplitude of displacement of the particles in the medium becomes $x$ times the initial value. The value of $x$ is

1. $5$
2. $3$
3. $2$
4. $6$

Q. The phase difference between the displacement wave and the pressure wave in sound wave is

1. $\frac{\pi }{3}$
2. $\frac{\pi }{2}$
3. $\frac{\pi }{4}$
4. $\frac{\pi }{6}$

Q. A sound wave of wavelength $40\text{cm}$ travels in air. If the difference between maximum and minimum pressures at a given point is $1.0\times {10}^{-3}{\text{N/m}}^2$, then find the amplitude of vibrations of the particles of the medium.
[Bulk modulus of air is $1.4\times {10}^5{\text{N/m}}^2$]

1. $3.3\times {10}^{-10}\text{m}$
2. $2.3\times {10}^{-10}\text{m}$
3. $4.3\times {10}^{-10}\text{m}$
4. $5.3\times {10}^{-10}\text{m}$

Q. What is the displacement amplitude of a sound wave having frequency of $100\text{Hz}$ and pressure amplitude $10\text{Pa}$?
[speed of sound in air $=340\text{m/s}$ and density of air $=1.29{\text{kg/m}}^3$]

1. $2.5\times {10}^{-5}\text{m}$
2. $3.6\times {10}^{-5}\text{m}$
3. $4.5\times {10}^{-5}\text{m}$
4. $1.5\times {10}^{-5}\text{m}$

Q. For a sound wave travelling towards +x direction, sinusoidal longitudinal displacement $\xi$ at a certain time is given as a function of x(Figure). If bulk modulus of air is $B=5\times {10}^{5}N/m^2$, the variation of pressure excess will be

1. 
2. 
3. 
4. 

Q. A sound wave of wavelength $40\text{cm}$ travels in air. If the difference between maximum and minimum pressures at a given point is $1.0\times {10}^{-3}{\text{N/m}}^2$, then find the amplitude of vibrations of the particles of the medium.
[Bulk modulus of air is $1.4\times {10}^5{\text{N/m}}^2$]

1. $3.3\times {10}^{-10}\text{m}$
2. $2.3\times {10}^{-10}\text{m}$
3. $4.3\times {10}^{-10}\text{m}$
4. $5.3\times {10}^{-10}\text{m}$

Q. For a sound wave travelling towards +x direction, sinusoidal longitudinal displacement $\xi$ at a certain time is given as a function of x(Figure). If bulk modulus of air is $B=5\times {10}^{5}N/m^2$, the variation of pressure excess will be

1. 
2. 
3. 
4. 

Q.

The pressure variation equation of a sound wave propagating in a medium with pressure amplitude $P_0$ is

$P=P_{0}sin\omega (t-\frac{x}{v})$

Inference:

In the tube where this wave is propagating if we measure pressure, then the maximum pressure measured will be _{$P_0$} atm and Minimum pressure measured will be _{$-P_0$} atm as maximum $\&$ minimum values of sin $\theta$ is (+1/-1).

1. Statement is correct, Inference is wrong
2. Statement is wrong, Inference is correct
3. Both Statement and Inference are correct
4. Both Statement and Inference are wrong