(1) Parasaurolophus was a dinosaur whose distinguishing feature was a hollow cre
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Question
(1) Parasaurolophus was a dinosaur whose distinguishing feature was a hollow crest on the head. The 1.2m long hollow tube in the crest had connections to the nose and throat, leading some investigators to hypothesize that the tube was a resonant chamber for vocalization. (Figure 1)
If you model the tube as an open-closed system, what are the first three resonant frequencies? (Use 350 m/s for the speed of sound.)
Enter your answers using two significant figures in ascending order separated by commas.
(2) Tendons are, essentially, elastic cords stretched between two fixed ends; as such, they can support standing waves. These resonances can be undesirable. The Achilles tendon connects the heel with a muscle in the calf. A woman has a 20-cm-long tendon with a cross-section area of 120mm2. The density of tendon tissue is 1100 kg/m3.
For a reasonable tension of 600N , what will be the fundamental resonant frequency of her Achilles tendon?
Express your answer to two significant figures and include the appropriate units.
Explanation / Answer
1)
Given that length L=1.2m
speed of the sound is v=350m/s
the first resonant frequency is
f1=v/4L
=350/4(1.2)
=72.91 Hz
the second resonant frequency is
f2=3(f1)
=218.75 Hz
the third resonant frequency is
f3=5(f1)
=364.58 Hz
So order is 72.91 Hz , 218.75 Hz, 364.58 Hz
2)
Given that Length L = 20 cm
Area of cross section is A = 120 mm^2 = 120*10^-6 m^2
density is ? = 1100
tension T = 600 N
? = M /L
= ??V / L
= ? A L / L
= ?A
fundamental resonant frequency is f = (1/ 2 L) * [sqrt (T / ?A) ]
f = (1/ 2*0.2)* [sqrt ( 600 / 1100*120*10^-6) ]
f = 168.55 Hz --> Answer
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