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Chapter 10: Problem 4

Do shallow waves propagate at the same speed in all fluids? Explain why or why not.

Short Answer

Expert verified
No, shallow waves do not propagate at the same speed in all fluids. The wave speed principally depends on the fluid's depth and the effect of gravity, not the nature of the fluid itself.

Step by step solution

01

Understanding Wave Propagation

Wave propagation indicates how waves move through a medium. In this situation, the mediums under consideration are fluids. Fluids can take the shape of their containers and include both gases and liquids. Shallow waves refer to waves that occur in a fluid medium with relatively lower depths compared to their wavelengths.
02

Examining the Speed Factors

The speed of wave propagation in a fluid, specifically shallow waves, depends on a few key factors. The gravity that pulls the wave downwards and the depth of the fluid are both pivotal influencers. The depth, in the context of shallow waves, implies that the speed will be governed by the square root of the product of the gravitational constant (g) and the depth (h): \(v = \sqrt{gh}\). Hence, the fluid's nature or characteristics don't explicitly feature into this equation.
03

Conclusion

Given that the speed equation doesn't reference any specific fluid characteristics, it can be gathered that shallow waves will propagate at the same speed in all fluids, assuming the depth and gravity remain the same across these different mediums. The fluid density or other fluid properties are not directly influencing the speed of the shallow wave.

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Most popular questions from this chapter

A rectangular brick-lined channel has a bottom slope of 0.0025 and is designed to carry a uniform water flow rate of \(300 \mathrm{ft}^{3} / \mathrm{s}\). Would the channel need fewer bricks if the channel were 2 ft wide, 6 ft wide, or \(10 \mathrm{ft}\) wide? Explain.

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