Concept explainers
Capillary waves (ripples) are small amplitude and wavelength waves, commonly seen, for example, when an insect or small particle hits the water surface. They are waves generated due to the interaction of the inertia force of the fluid ρ and the fluid surface tension σ. The wavelength is
Find the speed of capillary waves in water and mercury.
Want to see the full answer?
Check out a sample textbook solutionChapter 11 Solutions
Fox and McDonald's Introduction to Fluid Mechanics
Additional Engineering Textbook Solutions
Starting Out with C++ from Control Structures to Objects (9th Edition)
Computer Science: An Overview (13th Edition) (What's New in Computer Science)
Database Concepts (8th Edition)
Java: An Introduction to Problem Solving and Programming (8th Edition)
Modern Database Management
Web Development and Design Foundations with HTML5 (8th Edition)
- A transverse wave in a string has the form y= 5 cos pi ( 0.02x +3.00 t), where x is in centimeters and t is in seconds. The wave hits a stiff boundary and is reflected. Derive an equation for the resulting standing waves.arrow_forward(C) A small-amplitude wave is progressing in the positive x-direction on the surface of water of constant density p and depth h, so that the equation of the surface is z = n(x, t) where z is measured vertically upwards from the undisturbed surface (z = 0). = e sin(kx - wt) with € < 1, the pressure in the fluid can be You are given that for n(x, t) written P= Papgz + po, where Pa is the constant atmospheric pressure and is given by = eg sin(kx - wt) cosh[k(z + h)]/cosh(kh). Here k and w are related through the dispersion relation c = gk tanh kh. Consider the form of this flow in the shallow water limit, kh → 0. 1. What is the dispersion relation in this limit? 2. What is the wave speed? 3. Show that to leading order in kh the horizontal component of velocity is the same at all depths. 4. Show that to leading order in kh the vertical component of velocity varies linearly with depth, satisfying the kinematic boundary conditions on y = 0 and y = :-h.arrow_forwardThe equation of a wave in the international system SI, which propagates by a string is given by the expression: y(x,t)=0,08cos[2π(2x-4t)] Determine the velocity values at a point 2m from the source at the instant t=5s.arrow_forward
- A particle moving in one dimension is in a stationary state whose wave function is given as (x)=0 x<-a =A(1+cos(pi x)/(alpha)) -a<=x<a =0 x>a Where A a are real constants. (a) Is this a physically acepetable wave function? Explain (b)Find the magnitude of A so that wave function is normalizedarrow_forwardA traveling wave on a taut string with a tension force T is given by the wave function: y(x,t) = 0.1sin(4x+100t), where x and y are in meters and t is in seconds. The linear mass density of the string is u = 0.1 Kg/m. If the tension is multiplied by a factor of four, while keeping the same amplitude, same wavelength, and same !! linear mass density, then the new power of the wave, isarrow_forwardA 2-m sea wave has a 6 s period and occurs at the surface of 100-m deep water. Assume sea- water density equals to 1,025 kg/m³. Calculate the energy and power densities of the wave.arrow_forward
- 1. You hear a sonic boom and immediately look up to see where the plane is. Instead of a plane, you see an alien spacecraft 55° above the horizon. V sound sin a = Vsource (a) How fast is the alien spacecraft traveling? (b) If the alien spacecraft has an altitude of 6000 m, how long ago did it pass overhead? (c) Draw a picture of the soundwaves emitted by the alien spacecraft. Mark the interference that creates the shockwave.arrow_forwardDevelop an equation for the transmitted wave height behind a vertical wall extending a depth d into the water of depth h, based on the concept that the wall allows the wave power below depth d to propagate past. Qualitatively, do you believe that your equation for the transmitted wave height will under- or overestimate the actual wave height ? Discuss your results.arrow_forwardA traveling wave on a taut string with a tension force T is given by the wave function: y(x,t) = 0.1sin(4x+100t), where x and y are in meters and t is in seconds. The linear mass density of the string is u = 0.1 Kg/m. If the tension is multiplied by a factor of four, while keeping the same amplitude, same frequency, and same linear mass density, then the new power of the wave, is 1000 W O 2000 W O 250 W O 500 W 125 Warrow_forward
- At time = 0, a train wave has the from y= 4sin 2pie(x/100) the velocity is 30 cm/s. Find the equation for the wave form at time t = 2 sec.arrow_forwardIt is true, that lower frequency waves travel at a slower rate than high frequency sounds? Yes or no?arrow_forward2. Newton's derivation of the speed of sound assumed isothermal motion (dT/dt = = 0) and yielded an acoustic wave speed of (RT) / (gH)² where H RT/g is the isothermal scale height. We saw in class that the correct value is (7RT) ½. Replacing (de/dt 0), linearize the equations of motion and reproduce Newton's derivation. Use (d0/dt = 0) and other properties of a gas to prove mathematically that sound waves cannot propagate isothermally. 0) with (dT/dt = = =arrow_forward
- Elements Of ElectromagneticsMechanical EngineeringISBN:9780190698614Author:Sadiku, Matthew N. O.Publisher:Oxford University PressMechanics of Materials (10th Edition)Mechanical EngineeringISBN:9780134319650Author:Russell C. HibbelerPublisher:PEARSONThermodynamics: An Engineering ApproachMechanical EngineeringISBN:9781259822674Author:Yunus A. Cengel Dr., Michael A. BolesPublisher:McGraw-Hill Education
- Control Systems EngineeringMechanical EngineeringISBN:9781118170519Author:Norman S. NisePublisher:WILEYMechanics of Materials (MindTap Course List)Mechanical EngineeringISBN:9781337093347Author:Barry J. Goodno, James M. GerePublisher:Cengage LearningEngineering Mechanics: StaticsMechanical EngineeringISBN:9781118807330Author:James L. Meriam, L. G. Kraige, J. N. BoltonPublisher:WILEY