Find a combination of gravity waves (neglecting surface tension) on deep water travelling in the directions...

 

Transcribed Image Text:

Find a combination of gravity waves (neglecting surface tension) on deep water travelling in the directions a increasing and a decreasing that satisfies the conditions <= Co cos kr, ac/at = 0, at time t = 0, where is the upward displacement of the free surface at z = 0. In a deep and very long channel parallel to the z-axis, the water surface is distorted by the action of air jets into a shape S =-Soe-(x/a)² independent of y, and then released from rest at time t = 0. Obtain the subsequent shape of the free surface as a sum of two Fourier integrals. Use the method of stationary phase to obtain their approximate value when x and t are both large and positive. Find a combination of gravity waves (neglecting surface tension) on deep water travelling in the directions a increasing and a decreasing that satisfies the conditions <= Co cos kr, ac/at = 0, at time t = 0, where is the upward displacement of the free surface at z = 0. In a deep and very long channel parallel to the z-axis, the water surface is distorted by the action of air jets into a shape S =-Soe-(x/a)² independent of y, and then released from rest at time t = 0. Obtain the subsequent shape of the free surface as a sum of two Fourier integrals. Use the method of stationary phase to obtain their approximate value when x and t are both large and positive.

Answer rating: 100% (QA)

Another related effect is known as resonance In Oscillations we de... View the full answer