Assertion (A): If two waves of same amplitude produce a resultant wave of same amplitude, then the phase difference between them will be \(120^\circ\).
Reason (R): The resultant amplitude of two waves is equal to sum of amplitude of two waves.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
For two waves of amplitude \(A\) and phase difference \(phi\), the resultant amplitude is \(A_r = 2A \cos(\frac{\phi}{2})\). Given \(A_r = A\), so \(A = 2A \cos(\frac{\phi}{2})\), which means \(cos(\frac{\phi}{2}) = \frac{1}{2}\). Thus \(\frac{\phi}{2} = 60^\circ\), so \(\phi = 120^\circ\). Hence (A) is true. The resultant amplitude is the sum only if \(\phi = 0\). So (R) is false.
Assertion (A): Interference is position dependent phenomenon.
Reason (R): Beats is time dependent phenomenon.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
Interference describes the variation of intensity with position due to superposition of waves, so (A) is true. Beats describe the periodic variation in intensity with time at a point due to superposition of two waves with slightly different frequencies, so (R) is true. (R) does not explain (A).
Assertion (A): Interference can happen in sound waves.
Reason (R): In Quincke’s tube, interference is present due to initial phase difference as well as the phase difference due to path difference.
1. (1) Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. (2) Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (3) (A) is true but (R) is false
4. (4) Both (A) and (R) are false
View Answer
Sound waves, being waves, exhibit interference. Thus, Assertion (A) is true. In Quincke's tube, interference is primarily due to path difference. An initial phase difference is not typically considered in a standard setup. Therefore, Reason (R) is false.
Assertion (A): It is not possible to have interference between the waves produced by two violins of different frequency.
Reason (R): For interference of two waves, the phase difference between the waves must remain constant.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
Assertion (A) is true. For sustained interference, sources must be coherent, meaning same frequency and constant phase difference. Two violins produce incoherent waves. Reason (R) is true and correctly states the condition for interference.
Assertion (A): Energy is created during constructive interference and destroyed during destructive interference.
Reason (R): The positions of constructive interference are sources of energy while the positions of destructive interference are sinks of energy.
1. Both (A) & (R) are true and the (R) is the correct explanation of the (A)
2. Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
3. (A) is true but (R) is false
4. Both (A) and (R) are false
View Answer
Energy is always conserved in interference phenomena; it is merely redistributed, not created or destroyed. Thus, both Assertion (A) and Reason (R) are false.