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Concepts Of Physics MCQ Edition [Volume 1]
Exam
Concepts Of Physics MCQ Edition [Volume 1]
Subject
Physics
Chapter
Sound Waves

Concepts Of Physics MCQ Edition [Volume 1] · Physics · Sound Waves

The density and the bulk modulus of water are both greater than...

The density and the bulk modulus of water are both greater than those of air. Based solely on this information, it can be stated that the velocity of sound in air

Options

  1. Ais greater than its velocity in water
  2. Bis less than its velocity in water
  3. Cis equal to its velocity in water
  4. Dcannot be compared to its velocity in water

Correct answer

D. cannot be compared to its velocity in water

Step-by-step solution

The velocity of sound in a fluid medium is given by the formula:

v=Bρv = \sqrt{\dfrac{B}{\rho}}

where BB is the bulk modulus and ρ\rho is the density of the medium.

For water and air, the velocities are:

vw=Bwρwv_{w} = \sqrt{\dfrac{B_{w}}{\rho_{w}}} and va=Baρav_{a} = \sqrt{\dfrac{B_{a}}{\rho_{a}}}

It is given that Bw>BaB_{w} > B_{a} and ρw>ρa\rho_{w} > \rho_{a}.

Since both the numerator and the denominator for water are greater than those for air, the ratio Bwρw\dfrac{B_{w}}{\rho_{w}} could be greater than, less than, or equal to Baρa\dfrac{B_{a}}{\rho_{a}} depending on the actual numerical values of these quantities.

Therefore, based solely on the given information, the velocity of sound in air cannot be compared to its velocity in water.
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