Intensity of Sound Waves

Q. The equation of a wave motion is given by, $y=7\sin (7\pi t-0.4\pi x+\frac{\pi }{3})$. The ratio of wave velocity to the maximum particle velocity equal is
(Assume SI units)

1. $44:7$
2. $22:7$
3. $22:5$
4. $5:44$

Q. The faintest sound that can be heard has a pressure amplitude of about $4\times {10}^{-5}{\text{N/m}}^2$ and the loudest that can be heard without pain has a pressure amplitude of about $2.8{\text{N/m}}^2$. Determine the intensity of the faintest sound (both in ${\text{W/m}}^2$ and in $\text{dB}$).
[Assume, air density is $1.3{\text{kg/m}}^3$ and velocity of sound is $330\text{m/s}$ and take ${\log }_{10}1.86=0.269$]

1. $2\times {10}^{-12}{\text{W/m}}^2,1\text{dB}$
2. $1.86\times {10}^{-12}{\text{W/m}}^2,1.6\text{dB}$
3. $1.86\times {10}^{-12}{\text{W/m}}^2,2.7\text{dB}$
4. $2\times {10}^{-12}{\text{W/m}}^2,2.7\text{dB}$

Q. A point source emits sound of the same power in all directions in a non-absorbing medium. Two points $P$ and $Q$ are at a distance of $9\text{m}$ and $25\text{m}$ respectively from the source. The ratio of the amplitude of the waves at $P$ and $Q$ is

1. $\frac{3}{5}$
2. $\frac{5}{3}$
3. $\frac{9}{25}$
4. $\frac{25}{9}$

Q. If at some point, the amplitude of a sound wave becomes double and the frequency becomes one fourth, then at that point, the intensity of sound will:

1. Become double
2. Become half
3. Become one fourth
4. Remain unchnaged

Q. The displacement -time graphs for two sound waves $\text{A}$ and $\text{B}$ are shown in the figure. The ratio of their intensities $\frac{I_A}{I_B}$ is equal to

1. $1:4$
2. $1:16$
3. $1:2$
4. $1:1$

Q. Find the displacement amplitude of particles of air of density $1.5{\text{kg/m}}^3$ if the intensity and frequency of sound are $8\times {10}^{-6}{\text{W/m}}^2$ and $5000\text{Hz}$ respectively.
[speed of sound in air $=330\text{m/s}$]

1. $5.7\text{nm}$
2. $4.7\text{nm}$
3. $3.7\text{nm}$
4. $2.7\text{nm}$

Q. If the frequency of sound produced by a siren increases from $400\text{Hz}$ to $1200\text{Hz}$ keeping the amplitude constant. The ratio of the intensity of sound produced at frequency $1200\text{Hz}$ and $400\text{Hz}$ will be

1. $1:1$
2. $1:3$
3. $3:1$
4. $9:1$

Q.

A source of sound S and a detector D are placed at some distance from one another. A big cardboard is placed near the detector and perpendicular to the line SD as shown in figure. It is gradually moved away and it is found that the intensity changes from a maximum to a minimum as the board is moved through a distance of 20 cm. Find the frequency of the sound emitted. Velocity of sound in air is $336\frac{m}{s}$?

1. 1680 Hz

2. 420 Hz

3. 840 Hz

4. None of these

Q. The equation of a wave motion is given by, $y=7\sin (7\pi t-0.4\pi x+\frac{\pi }{3})$. The ratio of wave velocity to the maximum particle velocity equal is
(Assume SI units)

1. $22:5$
2. $5:44$
3. $22:7$
4. $44:7$

Q.

A longitudinal wave propagating in a water-filled pipe has intensity $3.00\times {10}^{-6}\frac{w}{m^2}$ and frequency 3400 Hz. Water has density $1000\frac{kg}{m^3}$ and bulk modulus $2.18\times {10}^9$ Pa. If the pipe is then filled with air at pressure $1.00\times {10}^5$ Pa and density $1.20\frac{kg}{m^3}$, and the a wave with the same intensity and frequency is propagated, What is the ratio of the two amplitudes in both media?

1. 4

2. 2.25

3. 1.75

4. None of these

Q.

Find the amplitude of vibration of the particles of air through which a sound wave of intensity $2.0\times {10}^{-6}W{m}^{-2}$ and frequency 1.0 kHz is passing. Density of air =$1.2kg{m}^{-3}$and speed of sound in air =$330m{s}^{-1}$

1. $1.6\times {10}^{-9}m$

2. $3\times {10}^{-8}m$

3. $1.6\times {10}^{-11}m$

4. None of these

Q.

A source of sound operates at$20kHz,20W$ emitting sound uniformly in all directions. The speed of sound in air is $340m{s}^{-1}$ and the density of air is $1.2kg{m}^{-3}$

(a) What is the intensity at a distance of $6m$ from the source?

(b) What will be the pressure amplitude at this point?

(c) What will be the displacement amplitude at this point?

Q.

The intensity of sound from a point source is $1.0\times {10}^{-6}{m}^{-2}$ at a distance of 5.0 m from the source. What will be the intensity at a distance of 25 m from the source?

1. $0.06\times {10}^{-8}W{m}^{-2}$

2. $0.08\times {10}^{-8}W{m}^{-2}$

3. $1\times {10}^{-8}W{m}^{-2}$

4. $0.04\times {10}^{-8}W{m}^{-2}$

Q. Match the following columns. Here, $I$ represent intensity, $A$ amplitude and $r$ distance from the source.

Column $\text{I}$	Column $\text{II}$
$a.$ $I$ due to point source	$p.$ $\propto r^{-1/2}$
$b.$ $A$ due to point source	$q.$ $\propto r^{-1}$
$c.$ $I$ due to line source	$r.$ $\propto r^{-2}$
$d.$ $A$ due to line source	$s.$ $\propto r^{-4}$

1. $a-r,b-q,c-q,d-p$
2. $a-p,b-q,c-r,d-s$
3. $a-q,b-q,c-s,d-r$
4. $a-r,b-p,c-q,d-r$

Q. In expressing sound intensity, we take ${10}^{-12}$ $W/m^2$ as the reference level. For ordinary conversation, the intensity level is about ${10}^{-6}$ $W/m^2$. Expressed in decibel, this is

1. ${10}^6$
2. 6
3. 60
4. $loge\left({10}^6\right)$

Q. Match the following columns. Here, $I$ represent intensity, $A$ amplitude and $r$ distance from the source.

Column $\text{I}$	Column $\text{II}$
$a.$ $I$ due to point source	$p.$ $\propto r^{-1/2}$
$b.$ $A$ due to point source	$q.$ $\propto r^{-1}$
$c.$ $I$ due to line source	$r.$ $\propto r^{-2}$
$d.$ $A$ due to line source	$s.$ $\propto r^{-4}$

1. $a-r,b-q,c-q,d-p$
2. $a-p,b-q,c-r,d-s$
3. $a-q,b-q,c-s,d-r$
4. $a-r,b-p,c-q,d-r$

Q. The pressure amplitude in a medium through which sound is travelling is $1.5\times {10}^{-3}{\text{N/m}}^2$ and intensity is ${10}^{-6}{\text{W/m}}^2$. If the pressure amplitude is increased to $4.5\times {10}^{-3}{\text{N/m}}^2$ by increasing the volume of sound then the intensity will be

1. $6\times {10}^{-6}{\text{W/m}}^2$
2. $7\times {10}^{-6}{\text{W/m}}^2$
3. $8\times {10}^{-6}{\text{W/m}}^2$
4. $9\times {10}^{-6}{\text{W/m}}^2$