Name: Stationary Wave in Closed and Open Organ Pipe
Uploaded: 2019-07-19
Duration: 11 min 39 s
Description: Organ pipes are musical instruments that produce a musical sound by blowing air into the pipe. Let's study the formation of stationary waves in organ pipes.

Question

What are the necessary conditions for the interference of sound waves? What do you understand by constructive and destructive interference?

Accepted Answer

Condition for interference:
(i) If the phase difference between the two waves at a point varies with time, then at one instant the two waves will meet at that same point in the same phase and at some other instant they will meet in opposite phases.
(ii) If the difference in amplitude of the waves is large then at the points where the waves meet in opposite phases, there will be sufficient intensity of sound.

Constructive interference: At points where the two interfering waves meet in the same phase(the phase difference between them is $0, 2 π, 4 π$ $, . . .$ )the resultant intensity is maximum. Its value $K {(a_{1} + a_{2})}^{2}$ is greater than the sum of the intensities $K ({a_{1}}^{2} + {a_{2}}^{2})$ of the two waves. At these points the resultant amplitude R is equal to the sum of the amplitudes $(a_{1} + a_{2})$ of the two waves. This is constructive interference.

Destructive interference: At points where the two interfering waves meet in opposite phase (the phase difference between them is $π, 3 π, 5 π, . . .$ ) the resultant intensity is maximum. Its value $K {(a_{1} ~ a_{2})}^{2}$ is less than the sum of the intensities of the two waves. At these points the resultant amplitude R is equal to the difference of the amplitudes $(a_{1} ~ a_{2})$ of the two waves. If the amplitudes of the two waves be equal $(a_{1} = a_{2})$ the resultant intensity at these points become zero. This is destructive interference.

G L Mittal and TARUN MITTAL Solutions for Chapter: Superposition of Waves-1 : Interference and Beats, Exercise 1: QUESTIONS

G L Mittal Physics Solutions for Exercise - G L Mittal and TARUN MITTAL Solutions for Chapter: Superposition of Waves-1 : Interference and Beats, Exercise 1: QUESTIONS

Questions from G L Mittal and TARUN MITTAL Solutions for Chapter: Superposition of Waves-1 : Interference and Beats, Exercise 1: QUESTIONS with Hints & Solutions

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