A piano consists of 88 keys each of which strikes one or more strings (though most keys have three strings). For the moment, assume that all of the strings have the same wave speed. The highest note on the piano has a frequency 4200 Hz, while the lowest note has a frequency 30 Hz. a.) Find the ratio of the lengths of the longest and shortest strings in the piano.
b.) If you open up a piano and measure the length of the shortest string, it is about 5 cm. If all strings have the same wave speed, what would the length of the longest string have to be?
c.) Based on your results, do you think all piano strings have the same wave speed? Explain.