Waves

Here, and is negative where is velocity of source and is velocity of listener (aeroplane)

If apparent frequency is and is actual frequency, then i.e., So, apparent frequency will increase, it means apparent wavelength will decrease.

Step 1: Use wave relation.
Wave speed is given by:

Step 2: Frequency remains constant.
When a wave enters a new medium, the frequency does not change because it is decided by the source.
Step 3: Compare old and new speed.
If speed doubles:

Step 4: Find the new wavelength.

But , so:

Final Answer:

Step 1: Use de Broglie wavelength relation.
For electron accelerated by potential , de Broglie wavelength is:

Step 2: Resolution required means wavelength should be comparable.
Given resolution \AA.
Step 3: Substitute in formula.



Step 4: Choose nearest option.
Closest option to 6 V is 5 V.
Final Answer:

Step 1: Understand beat frequency.
Beat frequency is the difference between the two frequencies heard by the listener.

Here, both sources emit same frequency .
Step 2: Apply Doppler effect.
Listener is moving away from both sources, but relative direction is different:
- From one source, listener is moving away frequency decreases.
- From the other source (if opposite direction considered), listener is moving towards frequency increases.
So:

Step 3: Find beat frequency.


Step 4: Substitute values.
Given: , , .


Final Answer:

Step 1: Energy and Wavelength.
In the photoelectric effect, the de-Broglie wavelength of an electron is inversely proportional to its momentum, which depends on the energy. As the energy is doubled, the wavelength will increase by a factor of .
Step 2: Explanation of Options.
(A) Incorrect: would not be , as energy increases.
(B) Correct: Doubling the energy causes the de-Broglie wavelength to increase by a factor of .
(C) Incorrect: The wavelength doesn't remain the same as energy changes.
(D) Incorrect: is not half of .
Step 3: Conclusion.
The correct answer is (B), .

Step 1: Identify the nature of electromagnetic waves.
Electromagnetic waves include gamma rays, X-rays, and cosmic rays. However, -rays are not electromagnetic waves; they are high-energy electrons emitted from radioactive decay.
Step 2: Conclusion.
Thus, -rays are not electromagnetic waves.
Final Answer:

For tubes with open and closed ends, the fundamental frequency is determined by the length and type of ends. Tube A has two open ends, while tube B has one closed end. The fundamental frequency for tube B is half that of tube A.
Final Answer:

Step 1: Use Faraday's Law of Induction.
According to Faraday’s Law, the induced emf is given by: where is the number of turns, is the magnetic flux, and is the rate of change of magnetic flux.

Step 2: Calculate the rate of change of flux.
Substituting the given values:

Step 1: Formula for Linear Momentum
The linear momentum of an object is given by: where is the mass and is the kinetic energy.
Step 2: Relationship Between Momentum and Mass
Given that the kinetic energies of the two masses are equal, we equate:
Rearranging:
Step 3: Substituting Values
Given g and g, we substitute: Final Answer: The ratio of the magnitudes of their linear momentum is 2:5.

Step 1: Understanding the Relation Between , , and
The refractive index of the prism is given by the equation: This equation helps in finding the angle of minimum deviation .
Step 2: Expressing in Terms of
We know that: Rearranging the equation, we get: Since we know that , we equate:
Step 3: Solving for
Simplifying the above equation: Thus, the angle of minimum deviation is given by: Final Answer: The angle of minimum deviation is .

Step 1: Understanding the Problem
The gold ring has an initial diameter of at room temperature ( ). It needs to expand to a diameter of to fit the wooden bangle. We need to find the temperature to which the ring must be heated.
Step 2: Using the Formula for Thermal Expansion
The change in diameter ( ) due to thermal expansion is given by: where: - (initial diameter), - (coefficient of linear thermal expansion), - is the change in temperature.
Step 3: Calculating the Change in Diameter
Step 4: Solving for the Change in Temperature Substituting the values:
Step 5: Calculating the Final Temperature Rounding off, the final temperature is approximately .
Step 6: Matching with the Options The closest option to our calculated value is (D) 152.7°C. Final Answer: The gold ring must be heated to 152.7°C.

Step 1: Understanding the Problem
We have a cylinder filled with water to a height of 20 m. A small hole is made near the bottom of the cylinder, and we need to find the velocity of efflux of water through this hole.
Step 2: Applying Torricelli's Law
The velocity of efflux ( ) of a fluid through a small hole at the bottom of a container is given by Torricelli's Theorem: where:
is the acceleration due to gravity ( ),
is the height of the fluid column above the hole (20 m in this case).
Step 3: Calculating the Velocity
Substitute the values into the formula:
Step 4: Matching with the Options
The correct option is (b) 20. Final Answer: The velocity of efflux of water is .

Step 1: Use the formula for the wavelength of a sound wave
The wavelength of a wave is given by the formula: where:
- is the speed of sound,
- is the frequency of the wave.
Step 2: Substitute the given values
We are given:
- Speed of sound ,
- Frequency .
Substitute these values into the formula: Answer: Therefore, the wavelength of the sound wave is . So, the correct answer is option (1).