15 assuming equal amplitudes gives mental s a cos at and s a

Last updated: 6/30/2023

15 assuming equal amplitudes gives mental s a cos at and s a cos w t 0 s are the one ency this ance ent ing nic ies 15 45 Here we have replaced the symbol y by s since we are referring to longitudinal not transverse displacement Let wo be the slightly greater of the two frequencies The resultant displacement is by the principle of superposition S S S a cosa t cos w t Using the familiar trignometric identity for cos A cosB we get ar ar t 2 which may be written as s 2 a cos w t cos w t 2 a cos COS and 2 az az t 2 If w w 1 w w w w th where 15 46 15 47 aj az 2 cca which means nation of the Shruti and Laya types Archaeologists date the Nelliappar temple to the 7th century and claim it was built by successive rulers of the Pandyan dynasty The musical pillars of Nelliappar and several other temples in southern India like those at Hampi picture Kanyakumari and Thiruvananthapuram are unique to the country and have no parallel in any other part of the world I asmen ut we can interpret Eq 15 47 as follows The resultant wave is oscillating with the average angular frequency however its amplitude is not constant in time unlike a pure harmonic wave The amplitude is the largest when the term cos at takes its limit 1 or 1 In other words the intensity of the resultant wave waxes and wanes with a frequency which is 20 0