Question

1. Students in a physics lab are asked to find the length of an air column in a tube close at one end that has a fundamental frequency of 341.3 Hz They hold the tube vertically and fill it with water to the top, then lower the water while a 341.3 Hz tuning fork is rung and listen for the first resonance. A. What is the air temperature if the resonance occurs for a length of 0.2483 m? (use velocity of sound: v= 331.4 m/s +0.6 x Tc) (3 pts.) B. At what lengths will they likely observe the 2nd, 3rd, and 4, resonances (1", 2nd, and 3rd, overtones)? (3 pts. C. The students next want to cut a pipe of the shortest length so that it resonates with the same tuning fork when open at both ends. How long should it be? (3 pts

Answer 1

For one end closed tube, resonance frequencies are given by, n2 f = 7 n = 1,3,5,... Given, fundamental frequency, fi= - = 341.3H2

A.

21 7 = 341312 . 331.4+0.6 x Tc 4 x 0.2483 -= 341.3 331.4+0.6 x TC = 338.97916 = 0.6 x TC =7.57916 TC = 12.63°C

B.

fn=nfi, v= 338.979m/s f2 = 682.6Hz, L= 338.979 4* 682.6 =0.1242m f3 = 1023.9Hz, L-_338.979 4 * 1023 0 = 0.0828m f4 = 1365.2H2, L 338.979 4* 1365.2 = 0.0621m

C.

For both ends open tube, fn = L = = 338.979 2f1 = 2 + 341.3 = 0.4966m