The directors of the Ufizzi museum decide to assassinate the curator of the Prad

Question

The directors of the Ufizzi museum decide to assassinate the curator of the Prado museum by producing 2 mostaccioli noodles ( hollow open at both ends) for him as a gift. They read an article which mentions that the curator's home will collapse if subjected to a sustained tone of 30 Hz. They hope that the wind blowing across the ends of the mostaccioli will produce sounds which will destroy his home. The speed of sound is 330 m/s

a) How long should the mostaccioli be to produce a 30 Hz frequency tone

b) The housekeep feels the house shaking as the mostaccioli begins to howl She chops each noodle into thirds and jams a sausage into one end of each noodle to form an open-closed pipe with length 1/3 length found in part a. Find the new fundamental frequency for the shorte stuffed noodle

c) Find the value for the next highest frequency that the stuffed noodles will resonate

Explanation / Answer

apply for open pipe frequency f = nv/2L

where v is speed

and L is length of the pipe

so

2L = 1 * 330/30)

2L = 11

L = 5.5 m

--------------------------------------------
frequency f of Closed pipe is f = nv/4L

here L = 5.5/3 = 1.833 m

so

f = 1 * 330/(4* 1.83)

f = 45.08 Hz

----------------------------------------

f2 = 3f1   for closed pipes

so

f2   = 3*45.08

f2 = 135.245 Hz

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