An ocean wave has a velocity of 20 m/s. (a) What is its period?
(b) What is its wavelength?
(c) If the energy per meter of wave front is $1 \mathrm { MJ }$ per period, what is the wave height?

Question

Quizplus · Accepted Answer

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

v = \frac { g T } { 2 \pi }

ext { So the period is given in terms of the velocity as }

T = \frac { 2 \pi v } { g } = \frac { 2 imes 3.14 imes ( 20 \mathrm {~m} / \mathrm { s } ) } { \left( 9.8 \mathrm {~m} / \mathrm { s } ^ { 2 } ight) } = 12.8 \mathrm {~s}

(b) The wavelength is

\lambda = \frac { g T ^ { 2 } } { 2 \pi } = \frac { \left( 9.8 \mathrm {~m} / \mathrm { s } ^ { 2 } ight) imes ( 12.8 \mathrm {~s} ) ^ { 2 } } { 2 imes 3.14 } = 256 \mathrm {~m}

(c) The energy per meter of wave front for one period is given in terms of the power as

E / l = P T / l

where

P / l = \left[ 1.96 imes 10 ^ { 3 } \mathrm {~W} / \left( \mathrm { m } ^ { 3 } \cdot \mathrm { s } ight) ight] H ^ { 2 } T

Solving for the wave height gives

H = \left[ \frac { E / l } { \left( 1.96 imes 10 ^ { 3 } \mathrm {~W} / \left( \mathrm { m } ^ { 3 } \cdot \mathrm { s } ight) ight) imes T ^ { 2 } } ight] ^ { 1 / 2 } = \left[ \frac { 10 ^ { 6 } \mathrm {~J} / \mathrm { m } } { \left( 1.96 imes 10 ^ { 3 } \mathrm {~W} / \left( \mathrm { m } ^ { 3 } \cdot \mathrm { s } ight) ight) imes ( 12.8 \mathrm {~s} ) ^ { 2 } } ight] ^ { 1 / 2 } = 1.76 \mathrm {~m}

An Ocean Wave Has a Velocity of 20 M/s 1MJ1 \mathrm { MJ }1MJ

An Ocean Wave Has a Velocity of 20 M/s $1 \mathrm { MJ }$