Question

Figure illustrates an arrangement employed in observations of diffraction of light by ultrasound. A plate light wave with wavelength `lambda = 0.55 mum` passes through the water-filled tank `T` in which a standing ultrasonic wave is sustained at a frequency `v = 4.7MHz`. As a result of diffraction of light by the optically inhomogemeous periodic structure a diffraction spectrum can be observed in the foacl plane of the objective `O` with focal length `f = 35 cm`. The separation between neighbouring maxima is `Deltax = 0.60mm`. Find the propegation velocity of ultrasonic oscillations in water.

Answer 1

When standing ulta sonic waves are sustained in the tank it behaves like a grating whose grating element is
`d=(v)/(v) =` wavelength of the ultrasonic
`v=` velocity of ultrasonic. Thus for maxima
`(v)/(v)sin theta_(m) = m lambda`
On the other hand
`f tan theta_(m) = m Deltax`
Assuming `theta_(m)` ti be small (beacuse `lambda lt lt (v)/(v))`
we get `Deltax = (f tan theta_(m))/(m) = (f tan theta_(m))/((v)/(v lambda) sin theta_(m)) = (lambda v f)/(v)`
or `v =(lambda v f)/(Deltax)`
Putting the values `lambda = 0.55mum, v = 4.7MHz`
`f = 0.35m `and `Deltax = 0.60 xx 10^(-3)m` we easily get
`v=1.51km//sec`.