What invention significantly changed communication speed through a workable telegraph?

The invention that significantly changed communication speed through a workable telegraph is the telegraph itself. The telegraph was developed in the early 19th century and allowed for the electrical transmission of coded messages over long distances. This revolutionized how people communicated, facilitating almost instantaneous communication compared to traditional methods like letter writing or messengers, which could take days or even weeks.

With the telegraph, messages could be sent using Morse code, a system of dots and dashes that represented letters and numbers. This technology laid the foundation for later advances in communication, making it possible for businesses, governments, and individuals to share information rapidly, which was crucial during events like the Civil War and the expansion of the railroads.

The other inventions listed, such as the telephone and the transatlantic cable, enhanced communication in significant ways; however, they came later and built upon the foundation that the telegraph established. The telephone, for instance, allowed for voice communication rather than coded messages, and the transatlantic cable extended the reach of telegraphic communication across oceans but did not change the basic technology of the telegraph itself. Therefore, the telegraph stands as the key invention that transformed communication speed in its time.