Parasaurolophus was a dinosaur whose distinguishing feature was a hollow crest on the head. The 1.5-m-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. If you model the tube as an open-closed system, what are the first three resonant frequencies?

f1 = 58.3Hz, f2 = 175Hz, f3 = 291.6Hz

Explanation:

lets assume speed of sound is 350 m/s.

frequencies of a standing wave modes of an open-close tube of length L

fm = m(v/4L)

where m is 1,3,5,7

and fm = mf1

where f1 = fundamental frequency

so therefore: f1 = 350 x 4 / 1.5

f1 = 58.3Hz

f2 = 3 x 58.3

f2 = 175Hz

f3 = 5 x 58.3

f3 = 291.6Hz

when jerome paddle in flowing river towards east the net speed of jerome will increase

so the net speed of jerome will be given as

now the speed of paul will be same as it is given as he is running on the ground

so

so here we can say since the speed of jerome is more so he will win the race

now as we know the distance so the time difference is given as

so jerome will reach first and the time difference will be 203.55 s or 3.4 min