A string of mass density μ = 7.30 × 10−3 kg/m is stretched horizontally between two fixed supports with a tension T = 1000 N, and two successive standing-wave frequencies are observed at 450 Hz and 540 Hz. There are other standing-wave frequencies lower than 450 Hz and higher than 540 Hz, but no others between. (a) What is the speed of transverse waves on the string? (b) What is the length of the string? (c) What is the frequency of the lowest standing-wave mode (first harmonic)?