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Question

A sound wave of wavelength 40 cm travels in air. If the difference between maximum and minimum pressures at a given point is 1.0×103 N/m2, then find the amplitude of vibrations of the particles of the medium.
[Bulk modulus of air is 1.4×105 N/m2
  1. 3.3×1010 m  
  2. 2.3×1010 m 
  3. 4.3×1010 m 
  4. 5.3×1010 m 


Solution

The correct option is B 2.3×1010 m 
Let P be the atmospheric pressure.
Difference between maximum and minimum pressures at a given point,
[(P+Po)(PPo)]=1.0×103 N/m2
2Po=1.0×103 N/m2
Po=0.5×103 N/m2
We know the relation between maximum value of pressure in the medium and displacement of the particles in the medium is given by,
Po=BAok
Ao=PoBk=λPo2πB 
Ao=40×102×0.5×1032×3.14×1.4×105 
Ao=2.3×1010 m 

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