3. The Stony Brook Swimming and Diving teams are aspiring PO experts, so they have decided...

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3. The Stony Brook Swimming and Diving teams are aspiring PO experts, so they have decided to determine how fast they would need to oscillate the water in their pool to resonate the water in it at its natural frequency. Assume that the pool is 50 m in length and is filled with water to a depth of 3 m. (a) Is the criteria for the seiche to be modeled as a shallow-water wave valid? (b) Assume the answer to (a) is Yes. Calculate what the natural frequency of oscillation would need to be to produce a seiche in the Stony Brook pool. How does this compare to what we found for a bathtub seiche in class? (c) Do you think 50 students (assume the pool is 6 lanes wide) could produce the seiche in the pool by swimming back and forth? Justify your answer. 3. The Stony Brook Swimming and Diving teams are aspiring PO experts, so they have decided to determine how fast they would need to oscillate the water in their pool to resonate the water in it at its natural frequency. Assume that the pool is 50 m in length and is filled with water to a depth of 3 m. (a) Is the criteria for the seiche to be modeled as a shallow-water wave valid? (b) Assume the answer to (a) is Yes. Calculate what the natural frequency of oscillation would need to be to produce a seiche in the Stony Brook pool. How does this compare to what we found for a bathtub seiche in class? (c) Do you think 50 students (assume the pool is 6 lanes wide) could produce the seiche in the pool by swimming back and forth? Justify your answer.