Mark the correct statement :

Options

A. In case of stationary waves the maximum pressure change occurs at antinode.
B. velocity of longitudinal waves in a medium is its physical characteristics .
C. Due to propagation of longitudinal wave in air , the maximum pressure change is equal to `2 pi n a//rho v`.
D. None of the above

Answer

B

Explanation

When a stationary wave is stablished in a medium then maximum deformation of the medium is produced at nodes . Hence , maximum pressure change takes place at nodes at antinodes ,no pressure change takes place . Therefore , option (a) is wrong .
` v = sqrt(("Elasticity")/("Density"))`
Since , elasticity and density both are the characteristic property of the medium , therefore , velocity of a longitudinal wave in a medium is its physical characteristic. So , option (b) is correct.
Due to propagation of longitudinal wave in a medium pressure change .
`Delta P = ( gamma P u)/(v)`
where `u` is the velocity of medium particles .
Pressure change will be maximum possible when medium particles have maximum possible velocity , which is equal to ` a omega = 2 pi n a`
Hence , `Delta P = gamma P ( 2 pi n a)/( v)`
But ` gamma P = rho v^(2)`
`:. Delta P = 2 pi n a rho v`
So , option ( c) and therefore option (d) is also wrong.