Wave Kinematics and Dynamics Questions and Answers

Q: A wave progresses up an estuary of decreasing water depth. If friction is neglected, then

The wave amplitude increases and wave length decreases.The tidal wave in an estuary is a long (shallow water) wave, travelling at c = √(gh). As the depth h decreases the wave slows down. Its period is fixed by the forcing, so its wavelength, cT, shortens.Without friction the energy flux is conserved. As the wave slows, the energy bunches up and the amplitude grows; in a channel of constant width it varies as h-1/4 (Green's law). The other options get one or both trends backwards.

Q: Tsunami is a shallow water gravity wave. A Tsunami has occurred over the ocean at a distance of about 1100 km from the coast. After how much time will it reach the coast ?

The key's answer is 1 hour 30 minutes, taking a typical open-ocean depth of about 4 km.A tsunami's wavelength is far greater than the ocean depth, so it travels as a shallow-water wave whose speed depends only on depth d:\[ \begin{aligned} v &= \sqrt{g d} = \sqrt{9.8 \times 4000} \\ &\approx 198\ \mathrm{m/s} \approx 713\ \mathrm{km/h} \\ t &= \frac{1100}{713} \approx 1.5\ \text{h} \end{aligned} \]The depth is not stated in the question, so the answer depends on assuming this typical depth; it agrees with the usual figure of 700 to 800 km/h for tsunamis in the deep ocean. One hour would need a speed of 1100 km/h (a depth of about 9.5 km), and two hours or more would need depths of about 2.4 km or less.

A wave progresses up an estuary of decreasing water depth. If friction is neglected, then

A.wave amplitude decreases and wave length increases
B.wave amplitude increases and wave length decreases
C.wave amplitude decreases and wave length decreases
D.wave amplitude increases and wave length increases

Exam Year(s)

GATE XE - 2018,

Answer: B

The wave amplitude increases and wave length decreases.

The tidal wave in an estuary is a long (shallow water) wave, travelling at c = √(gh). As the depth h decreases the wave slows down. Its period is fixed by the forcing, so its wavelength, cT, shortens.

Without friction the energy flux is conserved. As the wave slows, the energy bunches up and the amplitude grows; in a channel of constant width it varies as h^-1/4 (Green's law). The other options get one or both trends backwards.

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Tsunami is a shallow water gravity wave. A Tsunami has occurred over the ocean at a distance of about 1100 km from the coast. After how much time will it reach the coast ?

A.1 hour
B.1 hour 30 minutes
C.2 hours
D.2 hours 30 minutes

Exam Year(s)

MH SET - 2020, SET Exam - 2020,

Answer: B

The key's answer is 1 hour 30 minutes, taking a typical open-ocean depth of about 4 km.

A tsunami's wavelength is far greater than the ocean depth, so it travels as a shallow-water wave whose speed depends only on depth d:

\[ \begin{aligned} v &= \sqrt{g d} = \sqrt{9.8 \times 4000} \\ &\approx 198\ \mathrm{m/s} \approx 713\ \mathrm{km/h} \\ t &= \frac{1100}{713} \approx 1.5\ \text{h} \end{aligned} \]

The depth is not stated in the question, so the answer depends on assuming this typical depth; it agrees with the usual figure of 700 to 800 km/h for tsunamis in the deep ocean. One hour would need a speed of 1100 km/h (a depth of about 9.5 km), and two hours or more would need depths of about 2.4 km or less.

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