Two plane progressive waves having the same wavelength $\lambda$ and same frequencies with intensities $9{\mathrm{I}}_0$ and $4{\mathrm{I}}_0$ superimpose. Resulting intensity when the path difference between waves becomes $\frac{\mathrm{\lambda }}{4}$ is

A parallel beam of light is incident on a tank filled with water up to a height of $61.5 \mathrm{mm}$ as shown in the figure below. Ultrasonic waves of frequency $0.5 \mathrm{MHz}$ are sent along the length of the water column using a transducer placed at the top, and they form longitudinal standing waves in the water. Which of the schematic plots below best describes the intensity distribution of the light as seen on the screen? Take the speed of sound in water to be $1,500 \mathrm{m} {\mathrm{s}}^{-1}$.

Using monochromatic light of wavelength $\lambda$, an experimentalist sets up the Young's double slit experiment in three ways as shown.
If she observes that $y={\beta }^{\prime }$, the wavelength of light used is :