When a wave travels from one medium to another, it gets reflected at the boundary of the second medium. A common example of this is when a person yells at a distance from a cliff and hears the echo of their voice. The sound waves (longitudinal waves) traveling in the air are reflected from the bounding cliff. Similarly, flipping one end of a string whose other end is tied to a wall causes a pulse (transverse wave) to travel through the string, which gets reflected upon reaching the wall. In...

Sometimes waves do not seem to move; rather, they just vibrate in place. Unmoving waves can be seen on the surface of a glass of milk kept in a refrigerator, which is one example of standing waves. Vibrations from the refrigerator motor create waves on the milk that oscillate up and down but do not seem to move across the surface. These waves are formed or created by the superposition of two or more identical moving waves in opposite directions. The waves move through each other, with their...

Pozzolans are siliceous or aluminous materials blended with Portland cement. They interact with the calcium hydroxide produced during the hydration of Portland cement and contribute to improved strength and durability of concrete. The pozzolanic activity, a measure of a pozzolan's effectiveness, is typically assessed using the strength activity index, as defined in ASTM C 618-93, which calculates the ratio of the compressive strength of cement mixtures with and without pozzolan.
Fly ash is a...

A parabola is a fundamental curve in the family of conic sections arising from the intersection of a plane with a double-napped cone when the plane is parallel to the cone’s slant height. This geometric condition yields a unique open curve defined by its equidistance from a fixed point, the focus, and a fixed line, the directrix.A parabola is mathematically defined as the locus of all points in a plane that are equidistant from the focus and the directrix. In Cartesian coordinates, the standard...

The human heart is a complex organ made up of four chambers: the right and left atria and the right and left ventricles. These internal chambers are separated by partitions known as the interatrial and interventricular septa. The exterior of the heart features a groove known as the coronary sulcus that demarcates the atria from the ventricles, while the anterior and posterior interventricular sulci distinguish between the two ventricles.
Deoxygenated blood from the body is received in the right...

The starting point for expressing the modes of standing waves is understanding the boundary conditions that the waves must follow. The boundary conditions are derived from the physical understanding of how the standing waves are sustained, that is, how the vibrating particles of the medium behave at the boundaries imposed on them.
For a tube open at one end and closed at the other filled with air, the modes are such that there is always an antinode at the open end and a node at the closed end.