While deriving the Doppler formula for the observed frequency of a sound wave, it is assumed that the speed of sound in the medium is greater than the source's speed through it. When this condition is breached, a shock wave occurs.
When the source's speed approaches the speed of sound, constructive interference between successive wavefronts emitted by the source occurs immediately behind it. Initially, scientists believed that this constructive interference would result in such high pressures...

When a ligand binds to a cell-surface receptor, the receptor's intracellular domain changes shape, which may either activate its enzyme function or allow its binding to other molecules. The initial signal is amplified by most signal transduction pathways. This means that a single ligand molecule can activate multiple molecules of a downstream target. Proteins that relay a signal are most commonly phosphorylated at one or more sites, activating or inactivating the protein. Kinases catalyze the...

Unusual results are those that have a very low chance of occurring. Unusual results can be identified using probabilities and the range rule of thumb. In problems involving probability, unusual results can be observed in 2 instances – an unusually high number of successes or an unusually low number of successes.
According to the range rule of thumb, any value above or below two standard deviations, 2σ  from the mean, μ  is considered unusual.
Maximum unusual value = μ + 2σ
Minimum unusual value...

The z score is one of the three measures of relative standing. It describes the location of a value in a dataset relative to the mean. z scores are obtained after the standardization of the values in a dataset. The z score for the mean is 0.
 This score indicates how far a value is from the mean in terms of standard deviation. For example, if a data value has a z score of +1, the researcher can infer that the particular data value is one standard deviation above the mean. If another data value...

Many receptor binding ligands are hydrophilic; they do not cross the cell membrane but bind to cell-surface receptors. Thus, their message must be relayed by second messengers present in the cell cytoplasm. There are several second messenger pathways, each with its own way of relaying information. For example, the G protein-coupled receptors can activate both phosphoinositol and cyclic AMP (cAMP) second messenger pathways. The phosphoinositol pathway is active when the receptor induces...

Sound waves, which are longitudinal waves, can be modeled as the displacement amplitude varying as a function of the spatial and temporal coordinates. As a column of the medium is displaced, its successive columns are also displaced. As the successive displacements differ relatively, a pressure difference with the surrounding pressure is created. The gauge pressure varies across the medium.
The pressure fluctuation depends on the difference in displacements between the successive points in the...