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Write Sabine's formula explaining each term. Explain how this formula can be used for the determination of absorption co-efficient of a given material.
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Reverberation means the prolonged reflection of sound from walls, floor or roof of a hall. In simple language it is nothing but persistence of sound even after the sources of the sound has stopped.

 

Reverberation time:

The time gap between the initial direct note and the reflected note upto a minimum audibility level is called reverberation time.

 

Sabine’s formula

Prof. W.C. Sabine observed the concept of reverberation time for varieties of conditions like empty room, furnished room, small room, auditorium etc.

He concluded the following,

(a) Reverberation time depends upon reflectivity of sound form various surfaces available in side the hall. If the reflection is good, reverberation time of the hall will be longer as sound take more time to die out.

(b) Reverberation time depends upon volume of the hall.

                                     i.e.

(c) Reverberation time depends upon coefficient of absorption of various surfaces present in the hall. For shorter reverberation, absorption should be more.

(d) As absorption coefficient is found to be increased with increase in frequency, reverberation time decreases with frequency.

Reverberation time

where,

 Volume of hall

 Absorption

or

where,

 Proportionality constant

It has been further observed that is all the parameters are taken in SI then, proportionality constant is found to be 0.161.

…..(1.8)

Equation (1.8) is Sabine’s formula.

Absorption A given in Equation (1.8) represents overall absorption which is given as

 

Factors which determine average absorption co-efficient of a material-

 

1) Reverberation Time

  • If any material is to be acoustically satisfactory, it is essential that it should have the right reverberation time.
  • The reverberation time should be neither too long nor too short.
  • A very short reverberation time makes a room`dead’. On the other hand, a long reverberation time renders speechunintelligible.

The optimum value for reverberation time depends on the purpose for which a hall is designed

2) Loudness

  • Sufficient loudness at every point in the hall is an important factor for satisfactory hearing.
  • Excessive absorption in the hall or lack of reflecting surfaces near the sound source may lead to decrease in the loudness of the sound.

3) Focusing

  • Reflecting concave surfaces cause concentration of reflected sound, creating a sound of larger intensity at the focal point. These spots are known assound foci.
  • Such concentrations of sound intensity at some points lead to deficiency of reflected sound at other points.
  • The spots of sound deficiency are known asdead spots. The sound intensity will be low at dead spots and inadequate hearing.
  • Further, if there are highly reflecting parallel surfaces in the hall, the reflected and direct sound waves may form standing waves which leads to uneven distribution of sound in the hall.

4) Echoes

  • When the walls of the hall are parallel, hard and separated by about 34m distance, echoes are formed. Curved smooth surfaces of walls also produce echoes.

5) Echelon effect

  • If a hall has a flight of steps, with equal width, the sound waves reflected from them will consist of echoes with regular phase difference. These echoes combine to produce a musical note which will be heard along with the direct sound. This is calledechelon effect.
  • It makes the original sound unintelligible or confusing.

6) Noise

  • Noise is unwanted sound which masks the satisfactory hearing of speech and music.
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