Pressure Wave Derivation

Q. Pressure equation of a sound wave is $P=0.02\sin (3000t-9x)$ where all quantities are in $\text{SI}$ unit. The frequency and speed of sound wave is

1. $\frac{1000}{\pi }\text{Hz},500\text{m/s}$
2. $200\pi \text{Hz},500\text{m/s}$
3. $\frac{1500}{\pi }\text{Hz},\frac{1000}{3}\text{m/s}$
4. $100\pi \text{Hz},250\text{m/s}$

Q.

If the sound level in a room is increased from 50 dB to 60 dB, by what factor is the pressure amplitude increased ?

Q. A person blows into open-end of a long pipe. As a result, a high-pressure pulse of air travels down the pipe. When this pulse reaches the other end of the pipe

1. A high-pressure pulse starts traveling up the pipe, if the other end of the pipe is closed.
2. A high-pressure pulse starts traveling up the pipe, if the other end of the pipe is open
3. A low-prressure pulse starts traveling up the pipe, if the other end of the pipe is open
4. A low-pressure pulse stats traveling up the pipe, if the other end of the pipe is closed

Q.

Calculate the bulk modulus of air from the following data about a sound wave of wavelength 35 cm travelling in air. The pressure at a point varies between $(1.0\times {10}^{5}and14)$ Pa and the particles of the air vibrate in simple harmonic motion of amplitude $5.5\times {10}^{-6}$ m.

1. 1.4 x 10⁵ N/m²

2. 3.2 x 10² N/m²

3. 5.5 x 10⁶ N/m²

4. None of these

Q. Below figure represents the displacement y versus distance x along the direction of propagation of a longitudinal wave. The pressure is maximum at position marked

1. P
2. Q
3. R
4. S

Q.

For sound waves in air with frequency 1000 Hz, a displacement amplitude of $1.2\times {10}^{-8}$ m produces a pressure amplitude of $3.0\times {10}^{-2}$ Pa. What is the wavelength of these waves? (Provided Bulk modulus of Air = $1.42\times {10}^{5}Pa$)

1. 0.4 m

2. 0.3 m

3. 0.36 m

4. None of these

Q. For the pressure variation in a longitudinal wave represented as $P=P_o\cos (\omega t-kx)$, the density $\left(\rho \right)$ equation for the given medium is best represented by
(${\rho }_o$ is the density of the medium at pressure $P_o$)

1. $\rho ={\rho }_o\sin (\omega t-kx)$
2. $\rho =-{\rho }_o\sin (\omega t-kx)$
3. $\rho ={\rho }_o\cos (\omega t-kx)$
4. $\rho =-{\rho }_o\cos (\omega t-kx)$

Q. A sound wave is propagating through a medium and the displacement equation for the particles of the medium is given by $y=-A_0\sin (kx-\omega t)$ then which of the following options represents a possible pressure wave through this medium?

1. $\Delta P_o\sin (kx-\omega t)$
2. $\Delta P_o\cos (kx-\omega t)$
3. $-\Delta P_o\cos (kx-\omega t)$
4. $-\Delta P_o\cos (kx+\omega t)$

Q.

The equation of a sound wave in air is given by

$p=\left(0.01N{m}^{-2}\right)sin\left[\right(1000s^{-1})t-(3.0m^{-1}\left)x\right]$

(a) Find the frequency, wavelength and the speed of sound wave in air.

(b) If the equilibrium pressure of air is $1.0\times {10}^{5}N{m}^{-2}$, what are the maximum and minimum pressures at a point as the wave passes through that point.

$$\begin{array}{cc}& \\ \left(i\right)2.1& \left(p\right)\text{frequency in Hz}\\ \left(ii\right)1.0\times {10}^5+0.01& \left(q\right)\text{wavelength in m}\\ \left(iii\right)333& \left(r\right)\text{speed in m/s}\\ \left(iv\right)160& \left(s\right)\text{Max p in}N{m}^{-2}\end{array}$$

1. (p) - (iv); (q) - (i); (r) - (iii); (s) - (ii); (t) - (v)

2. (p) - (i); (q) - (ii); (r) - (iii); (s) - (iv); (t) - (v)

3. (p) - (iv); (q) - (v); (r) - (iii); (s) - (ii); (t) - (i)

4. (p) - (v); (q) - (ii); (r) - (i); (s) - (iii); (t) - (iv)

Q. The pressure amplitude in a sound waveform radio receiver is $2.0\times {10}^{-3}{\text{N/m}}^2$ and the intensity at a point is ${10}^{-8}{\text{W/m}}^2$. If by turning the "volume" knob the pressure amplitude is increased to $3\times {10}^{-3}{\text{N/m}}^2$. The intensity is equal to $x\times {10}^{-10}{\text{W/m}}^2$, where $x$ is:

1. 225
2. 250
3. 275
4. 300

Q. A sound wave of wavelength $50\text{cm}$ travels in a gas medium. If the difference between the maximum and minimum pressures at a given point is $5\times {10}^{-3}{\text{N/m}}^2$ and the amplitude of vibration of the particles of the medium is $5\times {10}^{-10}\text{m}$, find bulk modulus of the medium.

1. ${10}^5{\text{N/m}}^2$
2. $4\times {10}^5{\text{N/m}}^2$
3. $2\times {10}^5{\text{N/m}}^2$
4. $3\times {10}^5{\text{N/m}}^2$

Q. A man observed the pressure amplitude in a sound wave from a wireless receiver as $4\times {10}^{-2}{\text{N/m}}^2$ and the intensity at a point as ${10}^{-6}{\text{W/m}}^2$. If by turning the volume knob, the pressure amplitude is increased to $5\times {10}^{-2}{\text{N/m}}^2$, evaluate the intensity.

1. $1.25\times {10}^{-6}{\text{W/m}}^2$
2. $1.56\times {10}^{-6}{\text{W/m}}^2$
3. ${10}^{-6}{\text{W/m}}^2$
4. $2\times {10}^{-6}{\text{W/m}}^2$

Q. An electromagnetic wave passes through space and its equation is given by $E=E_0\sin (\omega t-kx)$ where $E$ is electric field. Energy density of electromagnetic wave in space is

1. ${\epsilon }_0{E}_0^2$
2. $\frac{1}{2}{\epsilon }_0{E}_0^2$
3. $2{\epsilon }_0{E}_0^2$
4. $\frac{1}{4}{\epsilon }_0{E}_0^2$

Q. A sound wave is propagating through a medium and the displacement equation for the particles of the medium is given by $y=-A_0\sin (kx-\omega t)$ then which of the following options represents a possible pressure wave through this medium?

1. $\Delta P_o\sin (kx-\omega t)$
2. $\Delta P_o\cos (kx-\omega t)$
3. $-\Delta P_o\cos (kx-\omega t)$
4. $-\Delta P_o\cos (kx+\omega t)$

Q. A sound wave in air has a frequency of 30 Hz and a displacement amplitude of $6.0\times {10}^{-3}mm$. For this sound wave the pressure amplitude (in Pa) is $467\times {10}^{-x}$. Find x.

1. 0.460 Pa
2. 10Pa
3. 50 Pa
4. 1 Pa

Q. A sound wave of wavelength $40\text{cm}$ travels in air. If the difference between the maximum and minimum pressure at a given point is $1\times {10}^{-3}{\text{Nm}}^{-2}$, find the amplitude of vibration of the particles of the medium. The bulk modulus of air is $1.4\times {10}^5{\text{Nm}}^{-2}$.

1. $2.2\times {10}^{-8}\text{m}$
2. $2.2\times {10}^{-9}\text{m}$
3. $2.2\times {10}^{-10}\text{m}$
4. $2.2\times {10}^{-11}\text{m}$

Q. A sound wave in air has a frequency of 30 Hz and a displacement amplitude of $6.0\times {10}^{-3}mm$. For this sound wave the intensity is $2.64\times {10}^{-x}W{m}^{-2}$. Find the value of x.

Q.

Calculate the bulk modulus of air from the following data about a sound wave of wavelength 35 cm travelling in air. The pressure at a point varies between $(1.0\times {10}^5\pm 14)$ Pa and the particles of the air vibrate in simple harmonic motion of amplitude $5.5\times {10}^{-6}m$.

Q. A small speaker delivers $2\text{W}$ of audio output. At what distance from the speaker, will one detect $120\text{dB}$ intensity sound ? [Given reference intensity of sound as ${10}^{12}{\text{W/m}}^2$]

1. $30\text{cm}$
2. $40\text{cm}$
3. $10\text{cm}$
4. $20\text{cm}$

Q. If the equations of two sound waves are $y_1=5\sin 252\pi t$ and $y_2=5\sin 281\pi t$ respectively. Then the number of beats heard per second will be

1. beats will not be heard
2. $6$
3. $12$
4. $34$

Q. A plane wave propagates along positive x-direction in a homogeneous medium of density $\rho =200kg/m^3.$ Due to propagation of the wave medium particles oscillate. Space density of their oscillation energy is $E=0.16{\pi }^{2}J/m^3$ and maximum shear strain produced in the medium is ${\varphi }_0=8\pi \times {10}^{-5}.$ If at an instant, phase difference between two particles located at points (1m , 1m , 1m) and (2 m , 2m , 2m) is $\Delta \theta ={144}^{\circ },$ assuming at $t=0$ phase of particles at $x=0$ to be zero,
Equation of wave is

1. $y={10}^{-4}sin\pi (400t-0.8x)$
2. $y={10}^{-4}sin\pi (2000t-0.8x)$
3. $y={10}^{-4}sin\pi (100t-8x)$
4. $y={10}^{-4}sin\pi (100t-2x)$

Q.

For sound waves in air with frequency 1000 Hz, a displacement amplitude of $1.2\times {10}^{-8}$ m produces a pressure amplitude of $3.0\times {10}^{-2}$ Pa. What is the wavelength of these waves? (Provided Bulk modulus of Air = $1.42\times {10}^{5}Pa$)

1. 0.3 m

2. 0.4 m

3. 0.36 m

4. None of these

Q. In Quincke's experiment, the sliding tube is pulled out by such a distance that sound intensity is changed from minimum to maximum. Find the ratio of the amplitudes of the two waves arriving at the detector, if maximum intensity is 16 times that of the minimum intensity.

1. 1 : 2
2. 2 : 1
3. 4 : 5
4. 5 : 3

Q. The maximum amplitude of an A.M. wave is found to be $15V$ while Its minimum amplitude is found to be $3V$. What Is the modulation Index?

Q. Two aeroplanes are travelling along parallel lines with the same velocity. The person in one aeroplane is hearing the sound of another aeroplane. If the ratio of actual frequency and apparent frequency of sound when two aeroplanes are approaching to each other is $4:5$, the ratio of actual frequency and apparent frequency of same sound when same two aeroplanes are moving away from each other is:

1. $5:6$
2. $6:7$
3. $5:9$
4. $5:4$

Q. For the pressure variation in a longitudinal wave represented as $P=P_o\cos (\omega t-kx)$, the density $\left(\rho \right)$ equation for the given medium is best represented by
(${\rho }_o$ is the density of the medium at pressure $P_o$)

1. $\rho ={\rho }_o\sin (\omega t-kx)$
2. $\rho =-{\rho }_o\sin (\omega t-kx)$
3. $\rho ={\rho }_o\cos (\omega t-kx)$
4. $\rho =-{\rho }_o\cos (\omega t-kx)$

Q. The equations of two displacement sound waves propagating in a medium are given by $s_1=2$ sin $\left(200\pi t\right)$ and $s_2=5$ sin $\left(150\pi t\right)$ The ratio of intensities of sound produced is :

1. 4:25
2. 64:225
3. 9:100
4. 8:15

Q. The pressure variation in a sound wave in air is given by
$\Delta P=12sin(8.18x-2700t+\pi /4)N/m^2$
Find the displacement amplitude. Density of air = $1.29kg/m^3$
Give answer in terms of 10${}^{-5}$ m

1. 2
2. 1.05
3. 5
4. 15

Q. An object of mass 0.2 kg executes SHM along the x-axis with frequency $\left(25/\pi \right)Hz$.At the point x=0.04m the object has KE 0.5 J and PE 0.4.J.The amplitude of oscillation (in cm) is

Q. A man observed the pressure amplitude in a sound wave from a wireless receiver as $4\times {10}^{-2}{\text{N/m}}^2$ and the intensity at a point as ${10}^{-6}{\text{W/m}}^2$. If by turning the volume knob, the pressure amplitude is increased to $5\times {10}^{-2}{\text{N/m}}^2$, evaluate the intensity.

1. ${10}^{-6}{\text{W/m}}^2$
2. $1.25\times {10}^{-6}{\text{W/m}}^2$
3. $1.56\times {10}^{-6}{\text{W/m}}^2$
4. $2\times {10}^{-6}{\text{W/m}}^2$