Tugas Superposisi Gelombang [PDF]

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TUGAS SUPERPOSISI GELOMBANG GELOMBANG



15 10 5 y1, y2, y3



I



0 -5



0



2



4



6



8



10



12



II III



-10 -15 x



Disusun oleh, Firsta Arianty Kamandika 140710120040 Geofisika 2012



I.



II.



PERSAMAAN GELOMBANG y1 = 2 sin π (8x - 100t) y2 = 10 sin π (8x - 100t)



:



Y SUPERPOSISI y superposisi (y3) = y1 + y2 =2 sin π (8x - 100t) + 10 sin π (8x - 100t) =2 sin (8πx - 100πt) + 10 sin(8πx - 100πt) Persamaan Trigonometri : Sin (A + B) = Sin A Cos B + Cos A Sin B Sin (A - B) = Sin A Cos B - Cos A Sin B Kita misalkan: A = 8πx dan B = 100πt y superposisi = 2 Sin (A - B) + 10 Sin (A - B) =2(Sin A Cos B - Cos A Sin B) + 10(Sin A Cos B - Cos A Sin B) =2 Sin A Cos B - 2 Cos A Sin B + 10 Sin A Cos B - 10 Cos A Sin B =12 Sin A Cos B – 12 Cos A Sin B =12(Sin A Cos B – Cos A Sin B) =12sin(A-B) y3 =12sin(8πx-100πt)



III.



PENGE-PLOT-AN y1 = 2 sin π (8x - 100t) DATA : A



k



w



2



8



100



GRAFIK



:



x 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10



t 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10



y1 1.8904184 1.2343117 -1.0844987 -1.942414 -0.1837624 1.8224299 1.3736824 -0.9255108 -1.9779766 -0.3659702 1.7390235 1.5014316 -0.7586931 -1.9968054 -0.5450819 1.6409048 1.6164786 -0.5854567 -1.9987411 -0.7195822



2.5 2 1.5 1 0.5 y1



0 -0.5 0



2



4



6



-1 -1.5 -2 -2.5 x



8



10



12



y2 = 10 sin π (8x - 100t) DATA : A



k



w



10



8



100



GRAFIK



:



x 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5



t 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5



y2 9.4520922 6.1715586 -5.4224937 -9.7120698 -0.9188122 9.1121493 6.8684118 -4.6275542 -9.8898828 -1.8298512



5.5 6 6.5 7 7.5 8 8.5 9 9.5 10



5.5 6 6.5 7 7.5 8 8.5 9 9.5 10



8.6951173 7.5071579 -3.7934654 -9.9840269 -2.7254096 8.204524 8.082393 -2.9272837 -9.9937056 -3.5979109



15 10 5 y2



0 0



2



4



6



-5 -10 -15 x



8



10



12



y3 = 12sin(8πx-100πt) DATA : A



k



w



10



8



100



GRAFIK



:



x 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5



t 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5



5.5 6 6.5 7 7.5 8 8.5 9 9.5 10



5.5 6 6.5 7 7.5 8 8.5 9 9.5 10



y3 11.34251 7.40587 -6.50699 -11.6545 -1.10257 10.93458 8.242094 -5.55307 -11.8679 -2.19582 10.43414 9.008589 -4.55216 -11.9808 -3.27049 9.845429 9.698872 -3.51274 -11.9924 -4.31749



6



8



15 10 5 y3



0 0



2



4



-5 -10 -15 x



10



12



SUPERPOSISI PLOT



:



15 10 5 y1, y2, y3



I



0 -5



0



2



4



6



8



10



12



II III



-10 -15 x



Terjadi superposisi pada gelombang y1 = 2 sin π (8x - 100t) dan y2 = 10 sin π (8x - 100t) menjadi y3 = 12sin(8πx-100πt). Terlihat bahwa setelah terjadinya superposisi, maka gelombang saling menguatkan terlihat dari amplitudonya yang menjadi 12.



DAFTAR PUSTAKA



http://4g0e5.files.wordpress.com/2012/12/lanjutan-bab-2b.pdf