Intense pulses in air: breakup of rotational symmetry

Identical bonds within a polyatomic group can stretch symmetrically (in-phase) or asymmetrically (out-of-phase). Similar to hydrogen bonding, these vibrations also influence the shape of the IR peak. Generally, asymmetric stretching frequencies are higher than symmetric stretching frequencies. For example, primary amines exhibit two distinct IR peaks between 3300–3500 cm−1 corresponding to the symmetric and asymmetric N-H stretching, while secondary amines exhibit a single stretching vibration...

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...

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.

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.

Irrotational flow is characterized by fluid motion where particles do not rotate around their axes, resulting in zero vorticity. For a flow to be irrotational, the curl of the velocity field must be zero. This imposes specific conditions on velocity gradients. For instance, to maintain zero rotation about the z-axis, the gradient condition:

The total change in the motion of an object is proportional to the total force vector acting on it and the time over which it acts. This product is called impulse, a vector quantity with the same direction as the total force acting on the object.
By writing Newton's second law of motion in terms of the momentum of an object and the external force acting on it, and simultaneously using the definition of the impulse vector, it can be shown that the total impulse on an object is equal to its net...