A Tsunami in Deep Water Has a Period Of$$5.7 \times 10 ^ { 2 } \mathrm {~s}$$

Question

Examlex · Accepted Answer

The Answer is (a) From equation (12.10) the velocity is

v = \frac { g T } { 2 \pi } = \frac { \left( 9.8 \mathrm {~m} / \mathrm { s } ^ { 2 } ight) imes \left( 5.7 imes 10 ^ { 2 } \mathrm {~s} ight) } { 2 imes 3.14 } = 889 \mathrm {~m} / \mathrm { s }

(b) The wavelength is

\lambda = \frac { g T ^ { 2 } } { 2 \pi } = \frac { \left( 9.8 \mathrm {~m} / \mathrm { s } ^ { 2 } ight) imes \left( 5.7 imes 10 ^ { 2 } \mathrm {~s} ight) ^ { 2 } } { 2 imes 3.14 } = 5.07 imes 10 ^ { 5 } \mathrm {~m} = 507 \mathrm {~km}

The power per length of wave front is

P / l = \left( 1.96 imes 10 ^ { 3 } \mathrm {~W} / \left( \mathrm { m } ^ { 3 } \cdot \mathrm { s } ight) ight) imes ( 2.5 \mathrm {~m} ) ^ { 2 } imes \left( 5.7 imes 10 ^ { 4 } \mathrm {~s} ight) = 6.98 \mathrm { MW } / \mathrm { m }

or

6.98 \mathrm { GW } / \mathrm { km }

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A Tsunami in Deep Water Has a Period Of $5.7 \times 10 ^ { 2 } \mathrm {~s}$