The contraction strength of muscles is regulated by motor neurons, which modulate the frequency of action potentials dispatched to the motor units based on the body's requirements. This process of varying the muscle stimulation frequency allows muscles to contract with a force that is precisely tailored to the needs of the moment, whether lifting a feather or a heavy box.
Wave summation
At low firing rates, motor neurons induce individual twitch contractions in muscle fibers. These twitches...

A wave propagates through a medium with a constant speed, known as a wave velocity. It is different from the speed of the particles of the medium, which is not constant. In addition, the velocity of the medium is perpendicular to the velocity of the wave. The variable speed of the particles of the medium implies that there must be acceleration associated with it. 
The velocity of the particles can be obtained by taking the partial derivative of the position equation with respect to time. We can...

The Doppler effect and Doppler shift were named after the Austrian physicist and mathematician Christian Johann Doppler in 1842, who conducted experiments with both moving sources and moving observers. Consider an observer standing on a street corner, observing an ambulance with a siren sound passing by at a constant speed. The observer experiences two characteristic changes in the sound of the siren. Initially, the sound increases in loudness as the ambulance approaches and decreases in...

When an oscillator is forced with a periodic driving force, the motion may seem chaotic. The motions of such oscillators are known as transients. After the transients die out, the oscillator reaches a steady state, where the motion is periodic, and the displacement is determined.

Understanding how an object moves along a path requires distinguishing between motion over a time span and motion at a precise moment. A useful example is a vehicle traveling along a straight and level path, where its position at any given time is known. The initial step in analyzing this motion is to measure how far the vehicle travels over a fixed time period. This measurement, called average velocity, is computed by dividing the total change in position by the duration over which the change...

The Doppler effect has several practical, real-world applications. For instance, meteorologists use Doppler radars to interpret weather events based on the Doppler effect. Typically, a transmitter emits radio waves at a specific frequency toward the sky from a weather station. The radio waves bounce off the clouds and precipitation and travel back to the weather station. The radio frequency of the waves reflected back to the station appears to decrease if the clouds or precipitation are moving...