The diagram shows a heat engine. in which area of the diagram is unusable thermal energy detected? w x y z

Nope, I disagree with the former answer. The answer is definitely Z. W area (boxed with red outline) is represented as the hot reservoir while Z area is the cold reservoir (boxed with blue outline). X area is the heat engine itself and Y area is the work produced from thermal energy from hot reservoir. Typically, all heat engines lose some heat to the environment (based from the second law of thermodynamics) that is symbolically illustrated by the lost energy in the cold reservoir. This lost thermal energy is basically the unusable thermal energy. The higher thermal energy lost, the less efficient your heat engine is. 

Z is the area of the diagram which has unusable thermal energy

detected.

What is Thermal energy?

This is also referred to as heat energy and it is responsible for

temperature differences in a body or area.

The Z region which is denoted by blue is referred to as the cold

region while the W region is the hot region. We know that since

heat is usually lost to the surroundings , then heat has been lost

to the Z region which is unusable and detected

Read more about Thermal energy here link

Wavelength divides in half and speed stays the same.