Problem 12.28 Constants Part A An organ pipe is 109 cm long. The speed of sound

Question

Problem 12.28 Constants Part A An organ pipe is 109 cm long. The speed of sound in air is 343 m/s. What are the fundamental and first three audible overtones if the pipe is closed at one end? Express your answers using three significant figures separated by commas. h./?.fs,A+ 787 236393551 ?? Correct Part B What are the fundamental and first three audible overtones if the pipe is open at both ends? Express your answers using three significant figures separated by commas. Submit X Incorrect: Try Again; 4 attempts remaining

Explanation / Answer

B.

If both ends are open, then you get a pattern of that are multiples of the fundamental,

At the fundamental, a both ends open organ pipe has a node in the middle, and two anti-nodes at each end, the length of the pipe (L) is equal to 2/4l, i.e.

L = l/2

l= 2L

= 2(1.09m) = 2.18 m,

Now fundamental frequency given as

f = v/l= (343 m/s)/(2.18 m) = 157.34 Hz
Successive frequencies are
f1 = 157 Hz (fundamental frequency)
f2 = 2f1 = 2 x 157.3 Hz = 315 Hz
f3 = 3f1 = 3 x 157.3 Hz = 472 Hz
f3 = 4f1 = 4 x 157.3 Hz = 629 Hz

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