The middle C string on a piano has a fundamental frequency of 262 Hz, and the string for the first A above middle C has a fundamental frequency of 440 Hz. 1. Calculate the frequencies of the next two harmonics of the C string. 2. If the A and C strings have the same linear mass density µ and length >, determine the ratio of tensions in the two strings. 3. If you look inside a real piano, you'll see that the assumption made in part (B) is only partially true. The strings are not likely to have the same length. The string densities for the given notes might be equal, but suppose the length of the A string is only 64% of the length of the C string. What is the ratio of their tensions?

The middle C string on a piano has a fundamental frequency of 262 Hz, and the string for the first A above middle C has a fundamental frequency of 440 Hz. 1. Calculate the frequencies of the next two harmonics of the C string. 2. If the A and C strings have the same linear mass density µ and length >, determine the ratio of tensions in the two strings. 3. If you look inside a real piano, you'll see that the assumption made in part (B) is only partially true. The strings are not likely to have the same length. The string densities for the given notes might be equal, but suppose the length of the A string is only 64% of the length of the C string. What is the ratio of their tensions?