Echo. Echo is the phenomenon of repetition of a sound due to its reflection from the surface of a large obstacle. When a loud sound is produced in an empty hall, the same sound is heard again after some time.
Conditions for the production of an echo:
(i) Sufficient time gap between original and reflected sounds. Due to persistence of hearing, we keep on hearing a sound for 0.1 s, even after reflected sound must reach the ear 0.1 s after the direct original sound.
(ii) Sufficient distance between the source of sound and the obstacle. The speed of sound in air is 344 m/s. The distance traveled by sound in\(0.1\quad s=344\times 0.1\times 0.1=34.4\quad m\) . So echo will be heard if the minimum distance between the source of sound and the obstacle =34.4/2=17.2 m.
(iii) Nature of the obstacle. For the formation of echo, the reflecting surface must be rigid such as a building, hill or cliff.
(iv) Size of the obstacle. Echoes can be heard if the size of the reflecting surface is quite large.

Time period. The time taken by an oscillating body to complete one oscillation is called its time period. It is denoted by T. Its SI unit is second (s).
Frequency. The number of oscillations or vibrations completed by an oscillating body in one second is called its frequency. It is denoted by v (Greek letter nu).
SI unit of frequency=per second (s^-1) = cycles per second (cps) = hertz (Hz).
Relation between time period and frequency:
Let T=time period of an oscillating body. Then number of oscillations completed in T second = 1
Number of oscillations completed in 1 second =\(\frac { 1 }{ T } \)
But number of oscillations completed in 1 second = frequency (v)
∴ \(v=\frac { 1 }{ T } \)
Hence frequency is equal to the reciprocal of time period.

First, we find the time taken by the stone to reach the base of the tower. We use the relation,
\(s=ut+{1\over2}gt^2\)
But,  s = 500m,  u = 0,   g = 10m s^-2
500=0+\({1\over2}\)x10xt²
or \(t^2={500\over5}=100\)  or  t = 10s
Time is taken by sound to travel from the base of the tower to its top,
\(f'={Distance\over Speed\ of\ sound}={500m\over 340ms^{-1}}=1.47s\)
Total time after which the splash is heard
= t + t' = 10 + 1.47 = 11.47 s

Reverberation. When a sound is produced in a big hall or auditorium, the sound waves suffer multiple reflections from the walls, ceilings and other materials present in the hall. Due to this, the sound persists for some time even after the source has stopped producing sound. This persistence of sound due to repeated reflection is called reverberation.
Methods of reducing reverberation. In a big hall or auditorium, excessive reverberation is highly undesirable. It can be reduced by the following methods:
(i) By covering the walls and roof of the auditorium with sound absorbent materials like compressed fireboard, rough plaster, etc.
(ii) Providing open windows in the space.
(iii) Providing heavy curtains with folds.
(iv) By using good sound absorbing materials for the seats.

Sonic boom. When a body moves in air with a speed greater than the speed of sound, it is said to have a supersonic speed. Bullets and jet aircrafts etc. often travel at supersonic speeds.
When a source of sound travels through air at a supersonic speed, it leaves behind itself a conical region of disturbance which spreads continuously. A region consisting of a very high pressure layer followed by a lower pressure layer travels through the space together with the cone. This is called a shock wave. It carries a large amount of energy.
When a shock wave reaches a person, the variations in its air pressure produce a sharp and sound in his ears. This is called sonic boom.
The sonic booms from a high speed jet aircraft can break glass dishes, windowpanes and can even cause serious damage to a building.

Differences between mechanical and electromagnetic waves.

Human ear is sensitive to frequencies between 20 Hz to 20,000 Hz. This frequency range of hearing from 20 Hz to 20,000 Hz. is called audible range. We cannot hear sounds of frequencies less than 20 Hz and above 20,000 Hz.

Time taken by sound to travel from child to cliff  \(t=\frac { 4 }{ 2 } =2\quad s\)
Speed of sound in air, v = 340 m/s
Distance of cliff from the child = \(vt=340\times 2=680\quad m\) 

The number of waves contained in unit length of the medium is called 'wave number'.
Wave number, \(\overset { - }{ v } =\frac { 1 }{ \lambda } \).                  

Relationship between frequency, wavelength and wave velocity. Since wavelength is the distance traveled by the wave during the time a particle of the medium completes one vibration, therefore if  \(\lambda \) be the wavelength and T the time-period, then the wave travels a distance \(\lambda \) in time T. Hence \(Wave\quad velocity=\frac { Distance }{ Time } \) or \(v=\frac { \lambda }{ T } \)
or  \(\upsilon =v\lambda \) \(\left[ \because \quad \frac { 1 }{ T } =frequency\quad \left( v \right) \right] \)
∴ Wave velocity=Frequency x Wavelength.
The wave velocity in a number remains constant under the same physical conditions.

Sound waves force the medium particles to vibrate. Hence, these waves are known as mechanical waves. Sound waves propagate through a medium because of the interaction of the particles present in that medium.

Difference between a sound wave and lightwave:

Sound needs a medium to propagate. Since the moon is devoid of any atmosphere, you cannot hear any sound on the moon.