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7a. Express the fundamental frequency of a piano wire fixed at both ends in terms of...

7a. Express the fundamental frequency of a piano wire fixed at both ends in terms of its tension FT, length L, radius r, and the 3D mass density ρ of the wire material.

7b. Given: radius r = 0.375 × 10-3 m, length L = 0.501 m, and ρsteel = 7.86 × 103 kg/m3. What is the tension required for a steel piano string tuned to middle C (f = 261.626 Hz)?

8.One of the harmonic frequencies of tube A with two open ends is 325 Hz.The next-highest harmonic frequency is 390 Hz. (a) What harmonic frequency is next highest after the harmonic frequency 195 Hz? (b) What is the number of this next-highest harmonic?

9. One of the harmonic frequencies of tube B with only one open end is 1080 Hz.The next-highest harmonic frequency is 1320 Hz. (c) What harmonic frequency is next highest after the harmonic frequency 600 Hz? (d) What is the number of this next-highest harmonic?

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