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.

Answer 1

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