In which medium can ultrasonic vibrations be propagated only in the longitudinal mode?

Ultrasonic vibrations can propagate in different modes depending on the medium. The longitudinal mode involves vibrations occurring in the direction of the wave travel, which is particularly relevant for liquids and some solids.

In this case, machine oil is the correct answer because it is a liquid medium, and ultrasonic waves in liquids predominantly propagate in the longitudinal mode. In liquids, particles are closely packed together and can easily transmit compressional waves, which are characteristic of longitudinal propagation.

In contrast, while solid materials like aluminum, ice, and beryllium can also conduct ultrasonic waves, they can support both longitudinal and transverse (shear) waves. In solids, the presence of molecular structure allows for the generation of shear waves along with longitudinal waves, making it possible for both types of wave modes to exist. Therefore, liquids like machine oil are unique in their ability to support ultrasonic vibrations mainly in the longitudinal mode without transverse wave propagation.