DOes the Gigahertz of a computer matter?

Gigahertz measures the number of instructions a processor can execute per second. 2.4 GHz processor processes more number of instructions compared to 1.6 GHz processor in a given time frame.

Computer performance depends on lot of other factors also like RAM, HDD speed,.... A computer loaded with 2.4 GHz processor might be faster compared to a computer loaded with 1.6 GHz processor but it is not always true...

The hertz of a computers processor is how many computational cycles it can conduct in a second.

so 1.6ghz performs less computations than a 2.4ghz.

yes it does because 1.6ghz is 1600mhz or it can do 1.6 billion processes a second and 2.4ghz can do 2.4 billion processes a second so higher is better :)

yep. based on exactly what you said. If its dual core vs single core then things change.