Question

Assertion: Resonance is a special case of force vibration in which the natural frequency of vibration of the body is the same as the impressed frequency of external periodic force and the amplitude of force vibration is maximum.
Reason: The amplitude of forced vibrations of a body increases with an increase in the frequency of the externally impressed periodic force.
A) Both assertion and reason are correct and reason is the correct explanation of the assertion.
B) Both assertion and reason are correct but reason is not the correct explanation of the assertion.
C) Assertion is correct but reason is incorrect.
D) Both assertion and reason are incorrect.

Answer 1

Hint: Resonance is a term which is used with the vibration of a system. Remember how resonance occurs when an external force is applied to the system and causes the system to vibrate at higher amplitude.

Complete step by step answer:
Resonance is a phenomenon in which the amplitude increases when the frequency of a periodically applied external force (or a Fourier component of it) is equal to the natural frequency of that particular system.
Resonance occurs when the applied force’s frequency becomes nearly equal to the natural frequency of vibration of the body to which the force applied. During the resonance, the amplitude of the forced vibration reaches the maximum value. The frequency at which the resonance occur is known as the resonance frequency.
The given assertion is therefore correct.
The tendency of one body to force another adjoining or interconnected object into vibrational motion is defined as a forced vibration.
If the frequency of the externally impressed periodic force is increased, the amplitude of the forced vibration does not increase but it decreases.
That is, the given reason is incorrect.

So the final answer is option (C), Assertion is correct but reason is incorrect

Note: There are different types of resonances:
1. Mechanical resonance: It is defined as the mechanical system’s tendency to respond with a higher amplitude when the frequency of its oscillations matches that system’s natural frequency of vibration.
2. Acoustic Resonance: It is the resonance occurring in acoustic systems. The system amplifies sound waves whose frequency becomes close to its own natural frequencies of vibration.
Electrical Resonance: Electrical resonance occurs in a circuit at a particular resonant frequency when the impedances cancel each other