ncert solutions physics class 11th

Doppler Effect in class 11 chapter 14 waves refers to the variation in the wavelength or frequency of a wave in relation to an observer moving relative to the wave source. When the wave source moves toward the observer, the frequency increases, and waves are compressed. If the source moves away, the frequency reduces and the waves are stretched. The Doppler Effect can be observed with the sound of a passing train or ambulance. This concept is also used in medical imaging technologies like Doppler ultrasound, radar, and astronomy to find whether galaxies or stars are moving away or towards the Earth.

When two waves of the same amplitude, frequency and speed travel in opposite directions and collide with each other, then a standing wave is formed. It is usually seen in the bounded medium, like a string fixed at both ends. It is different from the travelling waves and does not appear to move along the medium. At fixed locations, it forms specific points called nodes (with zero displacement) and antinodes (with maximum displacement). It is an important concept in understanding musical instruments, resonance and wave behaviour in closed and open pipes. The standing waves help in visualizing how energy can be stored in waveforms.

Mechanical waves are of two types - transverse waves and longitudinal waves. It requires a medium to travel. The medium particles vibrate perpendicular to the direction of wave propagation in the case of transverse waves.  However, the particles oscillate parallel to the wave direction in the longitudinal waves as seen in sound waves. The sound waves propagate by exerting forces by the neighbouring particles. While the wave particles stay close to the original position, the energy is passed on through the interactions among the adjacent particles.

A disturbance that travels through the space or medium transferring energy without the net movement of particles is called a wave. Rather than moving along with the wave, the particles of the medium only oscillate about their mean position in a wave motion. The wave is fundamentally different as compared to the particle motion where the particles travel from one place to another. In a sound wave, the air molecules do not travel to the sound, they vibrate back and forth. The concept of wave motion is one of the most important concepts in knowing how energy is transmitted in various forms including light, sound and water waves.

The main difference between the real and ideal gases is with respect to the kinetic theory. The ideal gas follows assumptions of the kinetic theory but the real gases do not follow it, especially when the temperature is low and there is high pressure.

The following points are applicable in the case of real gases:

• Real gas molecules do have finite volume.
• In such cases, intermolecular forces such as Van there Waals forces become significant.

The average kinetic energy of the gas molecules is directly related to the temperature of the gas. The average kinetic energy of one gas molecule, according to the kinetic theory, is given by:

Here T is the absolute temperature in Kelvin, and K is the Boltzmann constant. This equation shows that the average kinetic energy of the gas molecules increases with an increase in temperature. It implies that temperature here is the measure of the average kinetic energy of the particles. The equation also reflects that when gas gets heated why it expands - all molecules move faster and exert more pressure on the container walls.

According to the NCERT Solutions for Class 11 Physics Chapter 12 Kinetic Theory, the pressure is exerted due to gas molecules' collisions with the walls of the container. Each gas molecule has a certain mass and velocity. According to Newton's law, when the molecules collide with a wall, it changes momentum and this change in momentum exerts a force on the container wall. By considering the collisions from all molecules over a period in a unit area, the average force per unit area is called pressure. Mathematically, pressure P is:

p is the gas density.