Question

A dynamic pressure variation (max pressure - min pressure) of 10 kpa was recorded for a progressive wave (regular wave) by a pressure gauge located 5m above the sea floor. If the period of dynamic pressure is five seconds and the water is 10 meters deep, and the density of sea water is 1025 kg/m³?

1.What is the wave length?
2.What is the wave height?

Answer 1

The wavelength of the wave is 156.52 meters. The wave height is 0.102 meters.

Step-by-step explanation:

To find the wavelength, we can use the formula:

wavelength = speed / frequency

Since the period of the dynamic pressure wave is 5 seconds, the frequency can be calculated as 1 / 5 = 0.2 Hz. The speed of the wave can be calculated as the square root of the product of the gravitational acceleration (9.8 m/s²) and the depth of the water (10 m), which is approximately 31.304 m/s. Plugging these values into the formula gives:

wavelength = 31.304 m/s / 0.2 Hz = 156.52 meters

Next, to find the wave height, we can use the formula:

wave height = dynamic pressure variation / (density × gravitational acceleration)

Plugging in the given values, we get:

wave height = 10 kPa / (1025 kg/m³ × 9.8 m/s²) = 0.102 meters