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...

No object with a finite mass can travel faster than the speed of light in a vacuum. This fact has an interesting consequence in the domain of extremely high gravitational fields.
The minimum speed required to launch a projectile from the surface of an object to which it is gravitationally bound so that it eventually escapes the object’s gravitational field is called the escape velocity. The escape velocity is independent of the mass of the object. Merging the idea of escape velocity with the...

Although black holes were theoretically postulated in the 1920s, they remained outside the domain of observational astronomy until the 1970s.
Their closest cousins are neutron stars, which are composed almost entirely of neutrons packed against each other, making them extremely dense. A neutron star has the same mass as the Sun but its diameter is only a few kilometers. Therefore, the escape velocity from their surface is close to the speed of light.
Not until the 1960s, when the first neutron...

The shape of a small drop of liquid can be considered spherical, neglecting the effect of gravity. This drop can further be considered as two equal hemispherical drops put together due to surface tension. The forces acting on the spherical drop are due to the pressure of the liquid inside the drop, the pressure due to air outside the drop, and the force due to the surface tension acting on the two hemispherical drops.

Elastic collision of a system demands conservation of both momentum and kinetic energy. To solve problems involving one-dimensional elastic collisions between two objects, the equations for conservation of momentum and conservation of internal kinetic energy can be used. For the two objects, the sum of momentum before the collision equals the total momentum after the collision. An elastic collision conserves internal kinetic energy, and so the sum of kinetic energies before the collision equals...

The gravitational acceleration of an object near the Earth's surface is called the acceleration due to gravity. It can be measured by conducting simple experiments on Earth. However, such an experiment is impossible to conduct on the surface of other planets.
Astronomical observations are thus used to measure the acceleration due to gravity on other planets. This can be determined by observing the effect of a planet's gravity on objects close to it. The crucial factor that helps in this...