Are the Amplitude and Period Calculations Correct for This Tsunami Model?

[tennistudof09]

Am i on the right track?

We have this problem for math class:

For an interval of 45 minutes, the tsunamis near Hawaii caused by the chilean earthquake of 1960 could be modeled by the equation y= 8 sin (pi/6)t, where y is in feet and t is in minutes.

a) find the amplitude and period of the waves b) If the distance from one crest of the wave to the next was 21 kilometers, what was the velocity of the wave?

I know the amplitude is 8 and 2pi/ (pi/6) came out to be 12, so I got 12 for the period. For question b, in order to get the velocity, should i just do 21 x (.75)?

 

[Mark44]

You should add units to the numbers you found. For example, the amplitude is 8 feet. The period is 12 whats?

If the distance from the crest of one wave to the next is 21 km, that has to relate to the period somehow.

 

[tennistudof09]

so therefore i would convert 12 minutes into hours, which allows me to get .2 hours. Then since velocity is distance/time, i'd get 21km/.2 hr, and would give me a solution of 105 km/hr. Did I do that correctly?

 

[Mark44]

Looks good to me. The wave crests are 21 km apart, and it's .2 hour between crests, so the wave is traveling at 105 km/hr. Notice that this is a lot different from your first answer, which was 15.75 km/hr.