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National Bird Day: Why Birds Matter to Us

National Bird Day is celebrated every year on 5 January . This day is observed to spread awareness about birds, their importance in nature, and the need to protect them. Birds are beautiful living beings and play a very important role in keeping our environment healthy. Origin of National Bird Day National Bird Day was first celebrated in the year 2002 . It was started by bird lovers and environmental groups to protect birds from dangers like deforestation, pollution, and illegal hunting. The main aim of this day is to teach people, especially students, why birds are important and how we can help save them. Why Is National Bird Day Celebrated Every Year? National Bird Day is celebrated every year because many bird species are disappearing due to human activities. Cutting trees, using plastic, pollution, and climate change are harming birds and their homes. This day reminds us that: Birds need protection Nature should be respected Everyone has a responsibil...
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Sabine Formula | Oscillations and Waves

Sabine Formula

Reverberation time

  • Reverberation is defined as persistence of audible sound after the source has been switched off.
  • The time for which sound persist is known as reverberation time.

Assumptions

  • Distribution of energy is uniform in all parts of the hall.
  • No interference of sound waves in the hall.
  • Absorption coefficient does not depend on the intensity of sound.
  • There is no loss of energy in air.

Derivation

  • Average energy density within the hall in all direction = u
  • Energy received by elementary volume dV = u dV

  • Consider an element of surface area ds of a plane wall.
  • Elementary volume at a distance r from the centre of ds in the direction θ from normal on ds = dV
  • Solid angle subtended by surface element at elementary volume, dω = ds cos θ / r2
  • Area of shaded elementary portion = dr × r dθ
  • If the whole figure is rotated about the normal by an angle 2π then the elementary volume trace by this portion
                dV = elementary area × circumferential path
                      = dr . rdθ × 2πr sin θ
                      = 2πr2 sin θ dr dθ
  • Sound energy in volume dV 
                u dV = u × 2πr2 sin θ dr dθ
  • The fraction of this energy incident on area ds

  • Energy received by ds due to whole shell lying between two hemispheres for all values of θ
                    
  • Energy received per second by ds
                    
  • Here v = speed of sound in air
  • If a = absorption coefficient of ds, then
  • Energy absorbed per second by ds
                                             
  • Total energy absorbed per second by hall
                  
  • Total absorption of all the surface within the enclosure A = Σ a ds
  • Total energy absorbed per second by hall = uvA/4
  • Since V is the volume of enclosure, therefore
  • Total sound energy in the room at any time = uV
  • Rate of increase of this energy
                
  • Rate of absorption of energy
                
  • Rate of emission of energy from the source = E

Growth of sound

  • When source starts of sounding, t = 0, u = 0

  • When t = ∞, u = umax     ⇒     umax = 4E / vA
  • u = umax [1 - exp (-βt)]

Decay of sound

  • When source is cut off, t = 0, u = umax, E = 0


Reverberation period (T)

  • u = umax [1 - exp (-βt)]
  • If t = T, u = 10-6 umax

  • But v = 340 m/s
                
  • Above formula is known as Sabine formula.
To know more about Sabine formula please click on https://youtu.be/Qe-M7HqzHV0
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