Wave I Rork Piano Saring The graphs shown above represent the variations in air
ID: 2037744 • Letter: W
Question
Wave I Rork Piano Saring The graphs shown above represent the variations in air pressure in the sound waves recorded by a microphone as functions of time t. Wave 1 represents the sound wave when the tuning fork has been struck wave when both the tuning fork and the piano string have been struck. wave 2 represents the sound wave when a particular piano string has been struck, and wave 3 represents the sound a. Brielfly explain why the peaks in wave 3 at time A and nearty times are relatively large. Briefly explain why the peaks in wave 3 at time B and nearby times are relatively small.Explanation / Answer
Both waves start having the same phase that is there first peak coincides. According to superposition principle, the total pressure will be the sum of the two. We can see that the two add up to produce double the amplitude. If the frequency and hence the wavelength of the waves was same, this would have been true for every point as all the crests and troughs of the waves would have co-incided. Now, if we look closely, we can make out that the wave 1 looks a little stretched as compared to the other. This means that they are not identical. They gradually go out of phase and the third peak of wave 1 coincides with the trough of the second. Hence, the addition of the two would lead to cancellation and hence the resultant wave has zero amplitude. Moving ahaead, the waves again come back in phase. As expected, this happens after 3 cycles of wave 1 where point A is located. We call this the point of constructive interference. Later after 3 cycles from here, we reach point B that represents destructive interference. This will continue giving a resultant wave which has a wave like variation of the amplitude which is termed beats. We can also see that in 3 cycles of wave 1, the waves go out of the phase but in 6 cycles of wave 1, they are back in phase. In 6 cycles of wave 1, wave 2 covers 7 cycles. This can help us in finding out the frequency difference between the two.
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