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[A] The Physics of Dinosaurs Explorer Stan Ting Waif has found a Parasaurolophus skull with a 70 cm long crest on the top. The crest has a passage shaped like that in the figure which gives a length of about 2.1 meters for the entire air passage. a) Suppose now that the animal could close the internal end, like we close our throat. That would give two different arrangements for the 2.1 meter long passage; both ends open and closed at one end. Calculate the fundamental (longest) wavelength for each case: both ends open: one closed end : b) Using 350 m/s for the speed of sound at body temperature, calculate the fundamental and next 2 frequencies for each of the 2 cases in part (b). c) A second Parasaurolophus has a skull which is 80% as large as the one above. If they both vocalize at the fundamental with both ends open, what would be the beat frequency heard by the smaller Parasaurolophus if the larger one is approaching it at 8 m/s ?

[A] The Physics of Dinosaurs Explorer Stan Ting Waif has found a Parasaurolophus skull with a 70 cm long crest on the top. The crest has a passage shaped like that in the figure which gives a length of about 2.1 meters for the entire air passage. a) Suppose now that the animal could close the internal end, like we close our throat. That would give two different arrangements for the 2.1 meter long passage; both ends open and closed at one end. Calculate the fundamental (longest) wavelength for each case: both ends open: one closed end : b) Using 350 m/s for the speed of sound at body temperature, calculate the fundamental and next 2 frequencies for each of the 2 cases in part (b). c) A second Parasaurolophus has a skull which is 80% as large as the one above. If they both vocalize at the fundamental with both ends open, what would be the beat frequency heard by the smaller Parasaurolophus if the larger one is approaching it at 8 m/s ?

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[A] The Physics of Dinosaurs Explorer Stan Ting Waif has found a Parasaurolophus skull with a 70 cm long crest on the top. The crest has a passage shaped like that in the figure which gives a length of about 2.1 meters for the entire air passage. a) Suppose now that the animal could close the intenal end, like we close our throat. That would give two different arrangements for the 2.1 meter long passage; both ends open and closed at one end. Calculate the fundamental (longest) wavelength for each case: both ends open: one closed end : b) Using 350 m/s for the speed of sound at body temperature, calculate the fundamental and next 2 frequencies for each of the 2 cases in part (b). c) A second Parasaurolophus has a skull which is 80% as large as the one above. If they both vocalize at the fundamental with both ends open, what would be the beat frequency heard by the smaller Parasaurolophus if the larger one is approaching it at 8 m/s ? d) If the intensity of the fundamental in the open-open case is 15mW/m2 at a distance of 1.2 meters from the larger animal, calculate the power emitted from the nasal opening of the parasarolophus. If the area of the opening is 47 cm? ], what is the intensity of the sound wave there? If that area is constant for the outer passage, what is the intensity of the wave halfway (35 cm) up the outer passage ? e) What is the displacement amplitude of the fundamental for the closed-open case for the same animal in (e) at the nasal opening? Assume the only differences are the frequencies in the 2 cases. f) The rear legs of a parasaurolophus are 1.02 meters long, 37.5 cm in diameter at the top and 14.3 cm in diameter at the bottom. A leisurely walk has the leg swing through a 40 degree angle per step. Using a density of 0.88g/cm construct the integrals for the center of mass and moment of inertia of the leg and evaluate them (I suggest using software such as Wolfram Alpha to save time, although they are not difficult integrals). Using the results, determine the time for one swing of the leg, the distance of one step and the resulting walking speed. the period for the swing. Then calculate the distance per step and the walking Speedx Show all your work including setting up the integrals. You may use software such as Wolfram Alpha to do the integrals.
Transcribed Image Text:[A] The Physics of Dinosaurs Explorer Stan Ting Waif has found a Parasaurolophus skull with a 70 cm long crest on the top. The crest has a passage shaped like that in the figure which gives a length of about 2.1 meters for the entire air passage. a) Suppose now that the animal could close the intenal end, like we close our throat. That would give two different arrangements for the 2.1 meter long passage; both ends open and closed at one end. Calculate the fundamental (longest) wavelength for each case: both ends open: one closed end : b) Using 350 m/s for the speed of sound at body temperature, calculate the fundamental and next 2 frequencies for each of the 2 cases in part (b). c) A second Parasaurolophus has a skull which is 80% as large as the one above. If they both vocalize at the fundamental with both ends open, what would be the beat frequency heard by the smaller Parasaurolophus if the larger one is approaching it at 8 m/s ? d) If the intensity of the fundamental in the open-open case is 15mW/m2 at a distance of 1.2 meters from the larger animal, calculate the power emitted from the nasal opening of the parasarolophus. If the area of the opening is 47 cm? ], what is the intensity of the sound wave there? If that area is constant for the outer passage, what is the intensity of the wave halfway (35 cm) up the outer passage ? e) What is the displacement amplitude of the fundamental for the closed-open case for the same animal in (e) at the nasal opening? Assume the only differences are the frequencies in the 2 cases. f) The rear legs of a parasaurolophus are 1.02 meters long, 37.5 cm in diameter at the top and 14.3 cm in diameter at the bottom. A leisurely walk has the leg swing through a 40 degree angle per step. Using a density of 0.88g/cm construct the integrals for the center of mass and moment of inertia of the leg and evaluate them (I suggest using software such as Wolfram Alpha to save time, although they are not difficult integrals). Using the results, determine the time for one swing of the leg, the distance of one step and the resulting walking speed. the period for the swing. Then calculate the distance per step and the walking Speedx Show all your work including setting up the integrals. You may use software such as Wolfram Alpha to do the integrals.
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