Waves of length 12 m propagate in water of depth 3 m. Determine the phase velocity...
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.
Homework Answers
Add Answer to:
Waves of length 12 m propagate in water of depth 3 m. Determine
the phase velocity...
A progressive wave of height η1 = 0.05 m and wave length λ1 = 0.1 m...
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...
Waves of amplitude η 0 = 2 m and T = 2.5 s enter Tampa Bay at a...
Waves of amplitude η 0 = 2 m and T = 2.5 s enter Tampa Bay at a point where B = 1000 m and the depth h = 30 m. Determine the total available wave power. Use g = 9.8 m/s^2 and ρ = 1000 kg/m^3. Write the answer to the nearest tenth in units of: MW.
What is the phase speed (celerity) for a shallow water gravity wave of length 41 m,...
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
Consider a wave with a period of 22 seconds in a water depth of 2 m....
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
What is the period for a gravity-capillary wave of length 3 c m? Use the deep...
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
7. (i) The dispersion relation for surface water waves on deep water is given by w?...
7. (i) The dispersion relation for surface water waves on deep water is given by w? = gk. Show that the group velocity is Vg = g/(2w). Derive an expression relating the phase velocity Vp and the group velocity vg and hence determine if the dispersion is normal or anomalous. What are the physical significances of Vg and vp? [7 marks] Now consider a propagating wavepacket with initial length Lo. (ii) Use the bandwidth theorem to show that the minimum...
Capillary waves are waves that run across the surface of water because of the surface tension...
Capillary waves are waves that run across the surface of water because of the surface tension of the water. (You can see these waves if you gently touch your finger to the water surface in a glass of water.) If the surface tension of water is 0.07 Newtons/m, if the density of water is 1000 kg/m, and if the waves have a wavelength of 3 mm (waves this short aren't affected by gravity so ignore g), estimate the speed of...
Consider a semi-infinite canal with initial depth of 5 m and initial velocity of zero. A...
Consider a semi-infinite canal with initial depth of 5 m and initial velocity of zero. A pumping station at the (left) boundary of the canal starts withdrawing water as a result of which an expansion wave starts traveling along the canal. Consider a point on the expansion wave in which the velocity is -0.5 m/s. (a) Calculate the water depth at this point. (b) Determine the speed with which this point propagate along the canal. 1.
What is the period for a deep water gravity wave of length 10 m? Use the...
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
A stream has a width of 30 m, depth of 3 m, and a mean velocity...
A stream has a width of 30 m, depth of 3 m, and a mean velocity of 1.25 m's. authorities are planning to build a 1 m. a. Estimate the discharge (m/s) in the stream. b. Estimate the velocity of stream when the water level is c. How much head is generated when the water level is raised by 1 m? d. Determine if the weir has free or submerged discharge. 5. The stream sharp-crested weir to raise the water...
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...
7. (i) The dispersion relation for surface water waves on deep water is given by w? = gk. Show that the group velocity is Vg = g/(2w). Derive an expression relating the phase velocity Vp and the group velocity vg and hence determine if the dispersion is normal or anomalous. What are the physical significances of Vg and vp? [7 marks] Now consider a propagating wavepacket with initial length Lo. (ii) Use the bandwidth theorem to show that the minimum...
Consider a semi-infinite canal with initial depth of 5 m and initial velocity of zero. A pumping station at the (left) boundary of the canal starts withdrawing water as a result of which an expansion wave starts traveling along the canal. Consider a point on the expansion wave in which the velocity is -0.5 m/s. (a) Calculate the water depth at this point. (b) Determine the speed with which this point propagate along the canal. 1.
A stream has a width of 30 m, depth of 3 m, and a mean velocity of 1.25 m's. authorities are planning to build a 1 m. a. Estimate the discharge (m/s) in the stream. b. Estimate the velocity of stream when the water level is c. How much head is generated when the water level is raised by 1 m? d. Determine if the weir has free or submerged discharge. 5. The stream sharp-crested weir to raise the water...
Most questions answered within 3 hours.
-
A failure of an engine control unit causes it to fail an average
of 0.1 times...
asked 9 minutes ago -
A siren on an emergency car moving with velocity 90 km/hour
produces the sound with frequency...
asked 10 minutes ago -
Consider the schema below that models a bank’s branches,
customers and their accounts and loans. Provide...
asked 17 minutes ago -
What kinds of policies should be considered when individuals
decisions may likely impact public expense? For...
asked 26 minutes ago -
The financial statements of Apple Inc. show the following
numbers for fiscal year 2017 ($000,000):
Revenue...
asked 31 minutes ago -
Suppose that you are given the following results. Find the
correlation coefficient of the data.
sx...
asked 40 minutes ago -
The width of a tool used for semiconductor manufacturing
is assumed to be normally distributed with...
asked 42 minutes ago -
A
runaway train car that has a mass of 1,400 kg travels at a speed of...
asked 46 minutes ago -
The expected abnormal earnings of a firm that has earnings of
$40,000 with a required equity...
asked 45 minutes ago -
A spherical surface completely surrounds a collection of
charges. Find the electric flux through the surface...
asked 1 hour ago -
Two capacitors with capacitances of 12 and 18.1 µF,
respectively, are connected in parallel. The system...
asked 47 minutes ago -
Let's say you are a small business owner that provides
business-to-business software-as-a-service to non-profit
organizations. Your...
asked 51 minutes ago