Problem 5.132

Figure 5.27 illustrates an arrangement employed in observations of diffraction of light by ultrasound. A plane light wave with wavelength \(\lambda=0.55 \mu \mathrm{m}\) passes through the water-filled tank \(T\) in which a standing ultrasonic wave is sustained at a frequency \(v=4.7 \mathrm{MHz}\). As a result of diffraction of light by the optically inhomogeneous periodic structure a diffraction spectrum can be observed in the focal plane of the objective \(O\) with focal length \(f=35 \mathrm{~cm} .\) The separation between neighbouring maxima is \(\Delta x=\) \(=0.60 \mathrm{~mm} .\) Find the propagation velocity of ultrasonic oscillations in water.