We hear more clearly in a room with curtains than of that in a room without curtains because curtains act as a good sound absorbent. So, they absorb the sound produced in the room and thus, prevent unwanted echo of sound due to refraction. Otherwise, the inter lapping of sounds would be most undesirable as we won't be able to hear clearly.

Megaphone is based on multiple reflection of sound. It is a horn shaped tube designed to send amplified sound in a particular direction. It is also called Loud hailer.

Stethoscope is a medical diagnostic instrument based on multiple reflection of sound waves.
This is used by doctors for listening to the sounds produced inside the body.
Sound board is a concave rigid surface which is placed behind the speaker in a big hall so that his words can be heard clearly even by the people sitting away from the stage.

According to the definition of reverberation, it is the persistence of audible sound due to the successive reflections from the surrounding objects even after the source has stopped to produce that sound.

Reverberation time of a hall used by speeches should be very small so that due to multiple reflection of sound, we will hear the same voice again and again distracting our concentration to hear important points of the speech. If we hear same sound many times it will irritate us.

Sound boards are the curves surfaces (concave) which are used in a big hall to direct the sound waves towards the people sitting in a hall. The source of sound is placed at the focus of the sound board.

Reverberation is the phenomenon of persistence of sound after it has been stopped as a result of multiple reflections from surfaces such as furniture, people, air etc. within a closed surface. But the excessive reverberation is undesirable as the sound produced will continue to be heard repeatedly while the next sound being sent forth. This is unpleasant to hear and there is no clarity of sound.

Ear trumpet or hearing aid is used by the persons who are hard of hearing. The sound waves received by the wide end of the trumpet are reflected into a much narrower area.

Ceiling in a cinema hall is made curve so that the sound of music, dialogue etc must reach evenly to all the audience.
So that the sound after reflection from curved surface reaches all corners of the hall evenly.

Sound board is device which works on the reflection of light while others works on the reflection of sound.

Excessive reverberation in any auditorium or hall is not desirable because the sound becomes blurred and distorted. So the reverberation needs to be reduced.

Megaphones or loudhailers, horns, musical instruments such as trumpets and shehnais, are all designed to send sound in a particular direction without spreading it in all direction.
In these instruments, a tube followed by a conical opening reflects sound successively to guide most of the sound waves from the source in the forward direction towards the audience.

In concert halls, cinema halls, conference halls, the ceiling are made curved, so that the sound after reflection from the curved surface reaches all corners of the hall evenly.

Sound created in a big hall will persist  by repeated reflection from the walls until it is reduced to a value where it is no longer audible. The repeated reflection that results in this persistence of sound is called reverberation. In an auditorium or big hall excessive reverberation is highly undesirable.

Ceiling in a cinema hall is made curve so that the sound of music, dialogue etc must reach evenly to all the audience. So that the sound after reflection from the curved surface reaches all corners of the hall evenly.

Reverberation time of a hall used for speeches should be very short because multiple echoes will interfere with the original sound. So, reverberation time is reduced to avoid multiple echoes.

There is more reverberation in rooms with curtains so we can hear sound more clearly.

A certain amount of reverberation may improve the quality of sound. However, excessive reverberation is sometimes undesirable as it interferes with the original sound and hence makes the speech or music indinstict

Sound is not reflected equally from different materials. Hard surfaces reflects more sound.
Bad reflectors of sound are good absorbers. Soft thick curtains, thick carpets, holed card boards are examples of good absorbers of sound.

Megaphone, Stethoscope and Sound boards work on the reflection of sound.

Process in which sound waves bounces off obstacles and reflects many times before reaching destinations is known as multiple reflection of sound, So, all of the above are examples of multiple reflections of sound

Process in which sound waves bounces off obstacles and reflects many times before reaching destinations is known as multiple reflection of sound

In big rooms or halls,echos (due to multiple reflection of sound from the walls, roof, floor) follow so closely behind the original sound that the original sound appears to be prolonged even when the source of sound stops producing sound.

Sound waves travel differently at night than during the day. During the day, the sound bends away from the ground;during the night, it bends towards the ground. 

echo is heard due to reflection of sound and if obstacles are placed in path of sound then they will either absorb sound or will not perfectly reflect sound as before so echo will be not effective one .

Reverberation is the phenomenon of persistence of sound in a closed enclosure, due to multiple reflection of sound from the walls, even after the source has stopped producing sound. The intensity of sound gets reduced after each reflection.

The sound of a heartbeat ( or lungs ) reaches the doctor's ears by the multiple reflections of sound waves though the stethoscope tube.

Perforated card boards are used for the absorption of sound, as they are good sound absorbents and decrease reverberation time. 

A few window should be kept opened for the good absorption of sound in auditorium. Because if we open few windows, more sound will absorbed and more will be the sound clarity and better sound effect can be experienced. 

The reverberation time will get decreased because curtain will abrosh the sound and more sound will get abrashed then the earlier.  

The absorption coefficient of a body is the ratio of the heat radiation absorbed by the body to the total heat radiation incident on it. Since an open window can allow all the radiation into it, it is a good absorber. Hence its coefficient is highest.

Upholstered seats in cinema halls are arranged for better absorption of sound and to decrease the reverberation time. 

$R.T=\frac{1.61}{10}\times \frac{V}{A}$
=2.84se
=3 sec

since the halls and theatres are big enough so that we can distinguish between the generated sound and the reflected sound so the reverbereation  easily happens .

absorption of each visitor is 0.5
so, absorption for 1000 visitor is $1000\times 0.5$
$=500 metric sabine$

Time of reverberation $\propto$ $\frac{V} {A}$ (sabine's formula)

Volume of the room          $V = 100\times 40 \times 10 = 4\times 10^4      m^3$

A reverberation, or reverb, is created when a sound or signal is reflected causing a large number of reflections to build up and then decay as the sound is absorbed by the surfaces of objects in the space which could include furniture and people, and air. 

  We know that soft , porous and fibrous materials are good absorbers of sound , so they are used to the walls and ceiling of an auditorium to absorb the sound .

The multiple reflection of sound from the walls of a room or hall causing sound to persist for some time is called reverberation. If the hall is too long , the reflection will become an echo.

Let $d _{1}$ and $d _{2}$ be the distances of first and second cliff from man .

The pulse will be of same orientation as before after the phase change of $2\pi$ radians

$volume =240m^{3}$
$Area =27.2m^{2}+40\times 0.5m^{2}$
=47.2
$R.T.=0.161\times \frac{V}{A}$
=0.8186s

Given: $\dfrac{V _{1}}{V _{2}}=\dfrac{1}{8} \
\ \dfrac{A _{1}}{A _{2}}=\dfrac{1}{4}$
$R.T. _{1}=t $
$R.T=0.161\dfrac{v}{A}$
$\dfrac{R.T. _{1}}{R.T. _{2}}=\dfrac{0.161 \times \dfrac{v _1}{A _1}}{0.161 \times \dfrac{v _2}{A _2}}=\dfrac{v _{1}A _{2}}{v _{2}A _{1}}=\dfrac{1}{8}\times \dfrac{4}{1} =\dfrac{1}{2}$
$R.T _{2}=2R.T _{1}$
          $=2\times t$
          $=2t$ 

The reverberation time of the auditorium with volume V and total absorption coefficient A is given by:
$T _1=

\dfrac{0.17V}{A}$. Now when we will include n number of people each

having an absorption coefficient $A _p$ in the auditorium than the

reverberation time of the auditorium will be:
$T _2= \dfrac{0.17V}{A+nA _p}$. Now, here $A _p/A=1/1000$ and $n=500$ Using this two values the $T _2/T _1=2/3$.

let Area be A, when empty
let Area of audience be $A _{2}$ when full
so Area of cinema theatre when full $=A _{1}+A _{2}$
Area when half full $=A _{1}+\frac{A _{2}}{2}$
$R.T. \alpha \frac{1}{A}  ; \frac{R.T _{1}}{R.T _{2}}=\frac{A _{2}+A _{1}}{A _{1}}$
$3A _{1}=2A _{1}+2A _{2}  ; A _{1}=2A _{2} ; A _{2}=^{A _{1}}/ _{2}$
$R.T _{3}\alpha \frac{1}{A _{1}\frac{A _{2}}{2}} =\frac{4}{5 A _{1}}$
$ this \frac{4}{5} times     3 sec =2.4 sec$
 

The sensation of any sound persists in our ear for about 0.1 seconds. This is known as the persistence of hearing. If the echo is heard within this time interval, the original sound and its echo cannot be distinguished. So the most important condition for hearing an echo is that the reflected sound should reach the ear only after a lapse of at least 0.1 second after the original sound dies off. 
It is given that a pendulum has a frequency of $5$ vibrations per second. An observer starts the pendulum and fire a gun simultaneously. He hears echo from the cliff after $8$ vibrations of the pendulum which means that he hears the echo after 1.6 seconds. The speed of sound is given as $340 m/s$.
The distance traveled by sound of the gun shot in $1.6 $ seconds is calculated from the formula 
Distance traveled $=velocity\quad of\quad sound\times time\quad taken$. That is, $340 \times 1.6 $ = 544 m. This is twice the minimum distance between a source of sound (man) and the reflector (cliff) as it is reflected sound. 
So, the cliff is at a distance of 272 m least from the man, for the reflected sound or the echo to be heard distinctly in 1.6 seconds.

When a reflecting surface is less than 17 m away from the source, the echo that returns appears to be the original sound, just prolonged. This effect is called reverberation. The time interval between the original sound and the returning echo must be less than 0.1 seconds. It depends on the adsorption coefficient of the material which usually defines at 2048 Hz frequency.