A sonic source, located in a uniform medium, emits waves of frequency `n`. If intensity, energy density (energy per unit volume of the medium) and maximum speed of oscillations of medium particle are, respectively, `I`, `E` and `u_0` at a point, then which of the following graphs are correct?

Options

A.
B.
C.
D.

Answer

A, C, D

Explanation

If intensity at a point is `I`. Then energy density at that point is `E=(I)/(v)`, where `v` is wave propagation velocity.
It means that `EpropI`. Hence, the graph between `E` and `I` will be a straight line passing through the origin. Therefore, (a) is correct and (b) is wrong. Intensity is given by
`I=2pi^2n^2a^2rhov`
Hence, `E=2pi^2n^2a^2rho`
It means that `Epropn^2`
Hence, the graph between `E` and `n` will be a parabola passing through origin, having increasing slope and symmetric about E-axis, Hence, option (d) is correct.
Particle maximum velocity is
`u_0=aomega=2pina`
`impliespina=(u_0)/(2)`
Hence, `E=(1)/(2)rhou_0^2`
It means that graph between `E` and `u_0` will be a parabola, have increasing slope and will be symmetric about E-axis. Hence, option (c ) is also correct.