The process, that uses a tapered horn to amplify and focus the mechanical energy for machining of glass, is

The correct option is ultrasonic machining.

Explanation:
Ultrasonic machining (USM) is a non-traditional manufacturing process that is highly suitable for machining hard and brittle materials such as glass, ceramics, and quartz.

During the ultrasonic machining process, a high-frequency electrical signal is converted into mechanical vibrations by a transducer. These vibrations are typically in the frequency range of 20 kHz to 40 kHz. However, the amplitude of these vibrations produced by the transducer is relatively small, often on the order of a few micrometers.

To make the mechanical energy sufficient for machining, a tool holder known as a tapered horn (or concentrator) is used. The tapered horn acts as a mechanical amplifier. By gradually reducing its cross-sectional area from the transducer end to the tool end, it amplifies the amplitude of the longitudinal vibrations (focusing the mechanical energy) before delivering it to the machining tool.

The vibrating tool then forces abrasive slurry (a mixture of abrasive grits and water) against the workpiece surface. The repeated impact of the abrasive grains on the glass surface causes micro-chipping and erosion, thereby machining the glass into the desired shape.