What is the phase speed (celerity) for a shallow water gravity
wave of length 41 m, in water depth h = 2 m?
Use the shallow water approximation.
Use the following values for constants (if required):
g = 9.81 m/s^2,ρ = 1025 Kg/m^3, σ ′ = 0.072 N/m, π ≈ 3.14.
Write your answer in m s to the nearest thousandth

What is the phase speed (celerity) for a shallow water gravity wave of length 41 m,...
What is the period for a deep water gravity wave of length 10 m? Use the deep water approximation. Use the following values for constants (if required): g = 9.81 m/s^2 ,ρ = 1025 Kg /m^3, σ ′ = 0.072 N/m, π ≈ 3.14. Write your answer in seconds to the nearest thousandth
What is the period for a gravity-capillary wave of length 3 c m? Use the deep water approximation for capillary-gravity waves. Use the following values for constants (if required):g = 9.81 m/s^2 ρ = 1025 Kg/m^3, σ ′ = 0.072 N/m, π ≈ 3.14. Write your answer in seconds to the nearest thousandth
Consider a wave with a period of 22 seconds in a water depth of 2 m. What is the wave length of this wave? Use the following values for constants (if required): g = 9.81 m/s^2,ρ = 1025 Kg/m^3, σ ′ = 0.072 N/m, π ≈ 3.14. Write your answer in meters to the nearest tenth
Calculate phase speed of gravity waves propagating in the 20‐m deep ocean if the wave length is (i) 100 m; (ii) 30 m; (iii) 5 m. Which (if any) approximation do you use? How does it compare with the exact solution?
Waves of length 12 m propagate in water of depth 3 m. Determine the phase velocity AND group velocity of these waves. Ignore all interactions with the air. Phase speed is [c] m/s Use g = 9.8 m/s^2 and ρ = 1000 kg/m^3. Write the answer to the nearest tenth in units of: m/s.
Review | Constants Part A A water wave is a shallow-water wave if the water depth d is less than ~ 1/10. It is shown in hydrodynamics that the speed of a shallow-water wave is v= Vgd, so waves slow down as they move into shallower water. Ocean waves, with wavelengths of typically 110 m , are shallow-water waves when the water depth is less than 11 m. Consider a beach where the depth increases linearly with distance from the...
A progressive wave of height η1 = 0.05 m and wave
length λ1 = 0.1 m is generated at r1 = 0.5 m
away the center of a pond with a constant water depth of h = 2 m.
As the waves propagate away from the origin (where they are
generated), they become gravity–capillary waves. The dispersion
relation of gravity-capillary waves in deep water is given as
follows:
where σ ′ = 0.073 N/m is the surface tension for air–water...
Two pressure sensors are located as shown in the sketch. For an 8-s progressive wave, the dynamic pressure amplitudes at sensors 1 and 2 are 2.07 x 10 N/m and 2.56 x 10 N/m2, respectively. What are the water depth, wave height, and wave length? 4.9 Sensor 2 h Sensor 1 7.62 m Chap.4 Problems 129 The z axis is oriented vertically upward, that is, in a direction opposed to the gravity vector. The following values may be used: g=9.81...
A large aquarium of height 6 m is filled with fresh water to a depth of D = 2.50 m. One wall of the aquarium consists of thick plastic with horizontal length w = 7.80 m. By how much does the total force on that wall increase if the aquarium is next filled to a depth of D = 5.00 m? (Note: use g = 9.81 m/s2 and ρ = 998 kg/m3.)
What is the speed of a transverse wave in a rope of length 2.40 m and mass 59.0 g under a tension of 470 N? m/s