In general, sound wave frequencies do not increase with depth under water. In fact, the speed of sound in water decreases with depth, and this change in speed affects the propagation of sound waves.
The speed of sound in water is primarily influenced by temperature, salinity, and pressure. As you go deeper into the water, the pressure increases, and this leads to an increase in the speed of sound. However, the effect of increasing pressure on sound speed is relatively small compared to the decrease caused by the decrease in temperature with depth.
The decrease in temperature with depth causes the speed of sound in water to decrease as well. Since the speed of sound is inversely proportional to the wavelength of the sound wave, a decrease in speed results in an increase in wavelength. According to the wave equation (speed = frequency × wavelength), if the speed decreases and the wavelength increases, the frequency of the sound wave remains constant.
In summary, as sound waves propagate deeper into water, their frequencies do not increase. The speed of sound decreases with depth due to decreasing temperature, resulting in an increase in wavelength while keeping the frequency constant.