if there is a right solution please post. Thank you damental r frequency of the

Question

if there is a right solution please post. Thank you

damental r frequency of the pipe when one end is closed? d. What is the fundamental ate the solution A friend proposes a solution for the following p e the solution A friend proposes a solution for the following problem. 20.4.5 Evaluate the solution hlen: A violin A string is 0.33 m longand has mass 0.30 × 10-3 kg. It vibrates at a fun- problem: A violi The pr damental frequency of 440 Hz Proposed solution: Speed depends on the tension and string mass([T/m]). Thous ey of 440 Hz (concert A). What is the tension in the string? T = v2m = (340m/s)3(0.30 g) = 34,680 N a. Evaluate the solution and identify any errors. b. Provide a corrected solution if you find errors.

Explanation / Answer

Mass m = 0.3 * 10-3 kg

Length L = 0.33 m

Mass per unit length m' = 0.3 * 10-3 / 0.33 = 0.91* 10-3 kg/m

fundamental frequency f = 440 Hz

relation between f and length is:

f = v / 2L

v = wave speed

Thus, v = 2L * f = 2 * 0.33 * 440 = 290.4 m/s

Tension = T

relation between v and T:

v = square root (T/m')

Thus, T = v2 * m' = v2 * m/L = 290.42 * 0.91* 10-3 = 76.74 N

In the proposed solution the relation between tension and v is wrong as we divide T by mass per unit length and not mass.

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