Class 12 Dopplers effects Full Note

                              Dopplers effect Note

            Class 12

Doppler effect

Doppler Effect Solved Problems

Two trains A and B are moving toward each other at a speed of 432 km/h. If the frequency of the whistle emitted by A is 800 Hz, then what is the apparent frequency of the whistle heard by the passenger sitting in train B. (The velocity of sound in air is 360 m/s).

Solution:

The source and the observer are moving toward each other, hence.

$\begin{array}{l}�=\text{◂f()▸}\end{array}$

Converting 432 km/h into m/s we get 120 m/s.

Substituting the values in the equation, we get

$\begin{array}{l}\text{◂=▸}\end{array}$

Apparent frequency f = 1600 Hz

A bike rider approaching a vertical wall observes that the frequency of his bike horn changes from 440 Hz to 480 Hz when it gets reflected from the wall. Find the speed of the bike if the speed of sound is 330 m/s.

Solution:

Let the bike approach the wall with speed u.
goog_1947898177Then the apparent frequency received by the wall can be calculated as

$\begin{array}{l}\text{◂=▸}\dots (1)\end{array}$

For the reflected wave,

$\begin{array}{l}\text{◂=▸}\dots (2)\end{array}$

Substituting (1) in (2), we get

$\begin{array}{l}{�}^{\prime }=\text{◂+▸}\end{array}$

Simplifying, we get

$\begin{array}{l}\text{◂=▸}\end{array}$

Substituting the values in the equation, we get

$\begin{array}{l}480=\text{◂()▸}440\end{array}$

$\begin{array}{l}\frac{480}{440}=\text{◂()▸}\end{array}$

$\begin{array}{l}\text{◂=▸}\end{array}$

The speed of the bike is 14.3 m/s

Explain doppler effect in light. Distinguish between redshift and blueshift.

The Doppler effect in light is a phenomenon that occurs when there is relative motion between a light source and an observer. When the source and the observer are moving towards each other, the wavelength of the light waves emitted by the source appears shorter, which means that the frequency of the light waves appears higher. Conversely, when the source and the observer are moving away from each other, the wavelength of the light waves appears longer, which means that the frequency of the light waves appears lower.

Redshift and blueshift are two terms that describe the Doppler effect in light. Redshift occurs when a light source is moving away from an observer, which causes the wavelength of the light to appear longer, shifting it towards the red end of the spectrum. This effect is observed in objects that are moving away from us, such as galaxies that are moving away from the Milky Way.

Blueshift, on the other hand, occurs when a light source is moving towards an observer, which causes the wavelength of the light to appear shorter, shifting it towards the blue end of the spectrum. This effect is observed in objects that are moving towards us, such as stars that are approaching the Earth.

The amount of redshift or blueshift depends on the speed and direction of the relative motion between the source and the observer. The Doppler effect in light is a useful tool for astronomers to measure the speed and direction of objects in space, and to study the expansion of the universe.


The Doppler effect in light also plays a crucial role in understanding the properties of stars, planets, and other celestial bodies. For example, by analyzing the light spectrum of a star, astronomers can detect the presence of planets orbiting around it. This is done by observing the small changes in the star's spectrum caused by the planet's gravitational pull, which causes the star to wobble slightly.

Another important application of the Doppler effect in light is in cosmology. The redshift of light from distant galaxies was one of the key pieces of evidence used to support the theory of the Big Bang, which describes the origin and evolution of the universe. The redshift of light from these galaxies indicates that they are moving away from us, and the rate of this movement can be used to estimate the age and size of the universe.

In summary, the Doppler effect in light is a phenomenon that occurs when there is relative motion between a light source and an observer. It causes the wavelength and frequency of the light waves to change, resulting in either redshift or blueshift. This effect is useful in many areas of astronomy, including the study of stars, planets, and galaxies, as well as the origins and evolution of the universe.

 

 Some previous asked  important Questions for class 12

Unit One: Wave and Optics

1. What are stationary waves? Derive an equation for such a wave. [2060]
2. What the principle of superposition is as applied to wave motion? Discuss the result of superposing two waves of equal amplitude and same frequency travelling in opposite direction. [2068]
3. How is a progressive wave different from a stationary wave? Derive a progressive wave equation. [2070 ?D?]
4. What is Newton?s formula for the velocity of sound? What correction was made by Laplace? [2053]
5. Describe the various modes of vibrations of the air column in an organ pipe. [2054]
6. What is Doppler?s effect? Derive an expression for the apparent frequency received by a stationary observer when a source is moving away from him. [2057]

Unit Two: Physical Optics

1. State and explain Huygens?s principle to show that a plane wave front incident obliquely on a plane mirror is reflected as a plane wave front so that the angle of incidence is equal to the angle of reflection. [2060, 2068]
2. Define Michelson?s method to determine the speed of light. Write advantages of this method over Foucault?s method. [2067]
3. What are coherent source? Prove analytically that the bright and dark fringes in young?s double slit experiment are equally spaced. [2060]
4. Describe Young?s double slit interference experiment to determine the wavelength of the source of light. [2069]
5. What do you mean by polarization of light? Show that tan?_p = n_p where ?p is the angle of polarization and ? is the refractive index of the transparent medium. [2059]

Unit Three: Electricity and Magnetism

1. What do you mean by a shunt? Describe its use in converting a galvanometer into an ammeter. [2057]
2. What is drift velocity of an electron? Derive a relation between the current through a metallic conductor and the drift velocity in terms of the number of free electrons per unit volume of the conductor. [2059]
3. State and explain Ohm?s law. [2064]
4. What is potentiometer? Explain how do you compare emf of two cells using potentiontiometr. [2058]
5. What is a Wheatstone bridge? Obtain the balanced condition for the bridge. Explain how resistance can be measured by a meter bridge. [2068]
6. Explain, what do you mean by seebeck effect? How does thermoelectric emf vary with the temperature? [2057]
7. State and explain Faraday?s laws of electrolysis. Hence. Define Faraday?s constant. [2058]
8. Define the formula for the magnetic field at the centre of a circular coil carrying current. Explain why the magnetic field at the centre of the coil disappears when the circular coil is made infinitely large. [2059]
9. Derive an expression for the torque experienced by a current carrying rectangular coil placed in a uniform magnetic field and hence define magnetic dipole moment of the coil. [2060]
10. Derive an expression of force per unit length between two parallel conductors separated by a distance ?r? and carrying currents I₁ and I₂ in the same direction. [2066]
11. Define magnetic susceptibility and relative permeability and establish a relation between them. [2070 ?C?]
12. Obtain the expression for the emf induced in the conductor moving in a magnetic field. [2052]
13. State and explain Faraday?s law of electromagnetic induction. [2067]
14. An alternating e.m.f is applied across a capacitor. Show that the current in it leads to the applied e.m.f. by 90°

Unit Three: Modern Physics

1. Describe with necessary, theory, Millikan?s oil drop experiment to determine the value of the charge associated with an electron. [2052, 2068, 2069]
2. Describe an experiment to determine the specific charge of electron. [2054]
3. Explain the phenomenon of discharge of electricity through gases at low pressure. [2056]
4. Show that electron motion in magnetic field is circular. Prove that frequency and time period are independent with the velocity of electron. [2063]
5. How are P-type and N-Type semiconductors formed? Discuss the forward biasing of a P-N junction diode. [2060]
6. What is p-n-p transistor? Describe briefly a circuit of p-n-p transistor amplifier in its common emitted configuration. [2062]
7. What is Zender breakdown? Describe how a Zender diode can be used as a voltage regulator? [2070 ?C?]
8. What are X-rays? Confirm with experiment the wave nature of X-rays. [2055]
9. What are Bohr?s postulates? Derive the formula for the radius of the third Bohr?s orbit. [2059]
10. What are the postulates of Bohr atomic model? Obtain an expression for the energy of nth orbit of hydrogen atom. [2064]
11. State and explain Einstein?s mass energy relation with example. [2052]
12. Discuss fission and fusion with an example of each. In which reaction is the energy released greater? [2070 ?C?]
13. Explain the term ?artificial radio-isotopes?. [2054, 2054]
14. Discuss energy crisis in a modern society. [2062]