Tiêu đề 9. P1C9 HSC Prep Papers তরঙ্গ (With Solve) .pdf ✅

Zi1⁄2  HSC Prep Papers 1 Rhombus Publications Zi1⁄2 Wave beg Aa ̈vq HSC cixÿv_©x‡`i Rb ̈ evQvBK...Z m„Rbkxj cÖ‡kœvËi cÖkœ1 DÏxc‡Ki Zi1⁄2wU evav †c‡q cÖwZdwjZ n‡q GKB c‡_ wecixZ w`‡K wd‡i G‡m GKwU bZzb Zi1⁄2 m„wó n‡jv| [me KqwU ivwk SI GK‡K cÖKvwkZ] Y1 = 100 sin  (100t – 5x) m (K) `kv Kx? [Xv. †ev. 19] (L) k‡ãi ZxeaZv †j‡fj 20 dB ej‡Z Kx eyS? [Xv. †ev. 19] (M) DÏxc‡Ki Zi1⁄2wUi Zi1⁄2‣`N© ̈ KZ? [Xv. †ev. 19; Abyiƒc Xv. †ev. 17; h. †ev. 16] (N) DÏxc‡K m„ó bZzb Zi1⁄2wU‡Z m‡e©v”P we ̄Ív‡ii Ae ̄’vb ̧‡jv wbY©q Kiv m¤¢e wK-bvÑ MvwYwZKfv‡e we‡kølY Ki| [Xv. †ev. 19; Abyiƒc iv. †ev. 17] DËi: K Zi1⁄2w ̄’Z †Kv‡bv GKwU KYvi `kv ej‡Z H KYvi †h‡Kv‡bv gyn~‡Z© MwZi mg ̈K Ae ̄’v eySvq| L †Kv‡bv k‡ãi ZxeaZv I cÖgvY ZxeaZvi Abycv‡Zi jMvwi`g‡K IB k‡ãi ZxeaZv †j‡fj e‡j| k‡ãi ZxeaZv †j‡fj 20 dB ej‡Z †evSvq †Kv‡bv k‡ãi ZxeaZv I cÖgvY ZxeaZvi Abycv‡Zi jMvwi`‡gi `k ̧‡Yi mgvb| `ywU k‡ãi k‡ãv”PZvi cv_©K ̈ 20 dB n‡j †Rviv‡jv kã ÿxY k‡ãi †P‡q 100 ̧Y Zxea eySvq| M †`Iqv Av‡Q, Y1 = 100 sin  (100t – 5x) = 100 sin 5 (20t – x)...... (i) Avgiv Rvwb, AMÖMvgx Zi‡1⁄2i mgxKiY, Y = a sin 2  (vt – x) ...... (ii) (i) bs I (ii) bs mgxKiY Zzjbv K‡i cvB, 2  = 5   = 2 5   = 0.4 m myZivs, Zi1⁄2‣`N© ̈,  = 0.4 m (Ans.) N DÏxc‡K m„ó bZzb Zi1⁄2, Y = Y1 + Y2 = 100 sin  (100t – 5x) + 100 sin  (100t + 5x) = 100 [sin  (100t – 5x) + sin  (100t + 5x)] = 2  100 sin  (100t – 5x) + (100t + 5x) 2 cos  (100t – 5x) – (100t + 5x) 2 = 2  100  sin 100t  cos5x  Y = 200 sin 100t cos5x  Y = A sin 100t ; †hLv‡b, A = 200 cos5x m‡e©v”P we ̄Ív‡ii Ae ̄’v‡bi †ÿ‡Î, A =  200 m A_©vr, cos 5x =  1  5x = 0, , 2, ..., n [†hLv‡b, n = 0, 1, 2, ....]  x = 0, 1 5 , 2 5 , .... myZivs, 0, 1 5 , 2 5 , .... n‡e Zi1⁄2wUi m‡e©v”P we ̄Ív‡ii Ae ̄’vb| (Ans.) cÖkœ2 GKwU Zi‡1⁄2i mi‡Yi mgxKiY y (x, t) = 3 sin    36t + 0.018x +   4 . (K) w ̄úas aaæeK Kv‡K e‡j? [iv. †ev. 19] (L) eo eo njiæ‡gi †`qv‡j nvW©‡evW© wKsev cv‡U©· RvZxq †evW© jvMv‡bv nq †Kb? [iv. †ev. 19] (M) Zi1⁄2wUi ch©vqKvj wnmve Ki| [iv. †ev. 19] (N) x = 0 a‡i v-t MÖv‡di cÖK...wZ wKiƒc n‡e †Zvgvi gZvgZ wjL| [iv. †ev. 19] DËi: K †Kv‡bv w ̄úas Gi gy3 cÖv‡šÍi GKK miY NUv‡j w ̄úaswU mi‡Yi wecixZ w`‡K †h ej cÖ‡qvM K‡i Zv‡K H w ̄úas Gi w ̄úas aaæeK e‡j| L eo eo njiæ‡gi †`qv‡j nvW©‡evW© wKsev cv‡U©· RvZxq †evW© jvMv‡bv nq hv‡Z e3vi gyL †_‡K wbtm„Z k‡ãi DcwicvZb bv nq| eo eo njiæ‡gi †`qv‡j nvW©‡evW© wKsev cv‡U©· †evW© jvMv‡bv bv _vK‡j Kswμ‡Ui †`qv‡j kã Zi‡1⁄2i w ̄’wZ ̄’vcK msNl© nq d‡j Zv cÖvq mgvb ZxeaZv I †eM wb‡q wd‡i Av‡m Ges e3vi gyL wbtm„Z cieZ©x kã Zi‡1⁄2i Dci DcwicvwZZ n‡q Zv‡K weK...Z K‡i| d‡j e3vi K_v ̄úó nq bv| nvW©‡evW© wKsev cv‡U©· RvZxq †ev‡W©i Dci AvcwZZ kã Zi1⁄2 Lye mn‡RB †kvwlZ nq| Gi d‡j k‡ãi cÖwZdjb I cÖwZaŸwb Lye Kg nq| d‡j njiæ‡gi Af ̈šÍ‡i †Kvjvnjc~Y© cwi‡ek m„wó nq bv|

Zi1⁄2  HSC Prep Papers 3 Rhombus Publications DËi: K KwVb c`v‡_©i Aby ̧‡jvi g‡a ̈ wμqvkxj AvšÍtAvbweK ej‡K msmw3 ej e‡j| L Bqs Gi ̧Yv1⁄4 c`v‡_©i Dcv`v‡bi Ici wbf©i K‡i| GwU e ̄‘i •`N© ̈ cxob I •`N© ̈ weK...wZi AbycvZ| A_©vr †h cwigvY •`N© ̈ cxob cÖ‡qvM Kiv n‡j weK...wZ GK GKK nq, ZvB Bqs ̧Yv1⁄4| d‡j Bnv e ̄‘i AvK...wZi Ici wbf©i K‡i bv| AZGe GKwU †gvUv I GKwU wPKb B ̄úv‡Zi Zv‡ii Bqs Gi ̧Yv1⁄4 mgvb n‡e| M †`Iqv Av‡Q, A myikjvKvi †ÿ‡Î, Zi1⁄2‣`N© ̈, A = 3.2 m ch©vqKvj, TA = 0.01 s Avgiv Rvwb, k‡ãi †eM, vA = fAA = A TA = 3.2 0.01 = 320 ms–1 (Ans.) N †`Iqv Av‡Q, B myikjvKvi †ÿ‡Î, Zi1⁄2‣`N© ̈, B = 3. 05 m A myikjvKvi †ÿ‡Î, ch©vqKvj, TA = 0.01 s ÒMÓ bs n‡Z, k‡ãi †eM, v = vA = 320 ms–1 B myikjvKvi †ÿ‡Î, v = fBB  fB v B = 320 3.05 = 104. 92 Hz Avevi, A myikjvKvi †ÿ‡Î, fA = 1 TA = 1 0.01 = 100 Hz  fB – fA = 104.92 – 100 = 4.92 Hz <10 Hz myZivs, DÏxc‡Ki myikjvKv `ywU GK‡Î evRv‡j exU Drcbœ Ki‡e| (Ans.) cÖkœ5 P, Q I R wZbwU myikjvKv GKwU wbw`©ó gva ̈‡g ivLv n‡jv| P myikjvKvi 4wU c~Y© Zi1⁄2‣`N© ̈ Q-Gi 5wU c~Y© Zi1⁄2‣`‡N© ̈i mgvb| Zv‡`i g‡a ̈ K¤úv‡1⁄4i cv_©K ̈ 60 Hz| wKš‘ R myikjvKv Øviv m„ó AMÖMvgx Zi‡1⁄2i mgxKiY Y = 0.2 sin 2    100t –  x 15 m| (K) Abybv` Kv‡K e‡j? [P. †ev. 19; Abyiƒc mw¤§wjZ †ev. 18; w`. †ev. 17; iv. †ev. 16] (L) m1⁄2xZ ̧Y kã gvby‡li g‡b cÖkvwšÍ m„wó K‡i wbivc‡` iv‡LÑ e ̈vL ̈v Ki| [P. †ev. 19] (M) DÏxc‡Ki P I Q myikjvKvi K¤úv1⁄4 wbY©q Ki| [P. †ev. 19; Abyiƒc h. †ev. 16] (N) Kx c`‡ÿc wb‡j R myikjvKvi Zi1⁄2 Øviv w ̄’i Zi1⁄2 cvIqv hv‡e? MvwYwZKfv‡e we‡kølY Ki| [P. †ev. 19; Abyiƒc Kz. †ev. 17] DËi: K ciek K¤ú‡bi we‡kl †ÿ‡Î hw` e ̄‘i wbR ̄^ K¤úv1⁄4 I ciek m„wóKvix ch©vqe„Ë e‡ji K¤úv1⁄4 ci ̄ú‡ii mgvb nq Z‡e e ̄‘ weivU we ̄Ív‡i Kw¤úZ nq| G‡K Abybv` (resonance) e‡j| L †h kã ïb‡j fvj jv‡M Zv‡K kÖæwZgayi, myihy3, myimg„× ev mykÖve ̈ kã e‡j| m1⁄2xZ ̧Y k‡ãi Dr‡mi K¤úb wbqwgZ ch©vqe„Ë Ges wbiew”Qbœ nIqvq gvby‡li g‡b cÖkvwšÍ m„wó K‡i Ges i3Pvc ̄^vfvweK ivL‡Z mvnvh ̈ K‡i| Aciw`‡K kÖæwZKUz, myiewR©Z ev †Kvjvnj Dr‡mi K¤úb AwbqwgZ, Ach©vqe„Ë Ges AvKw ̄§K nq| G ai‡bi kã gvby‡li gb‡K wLUwL‡U K‡i †Zv‡j Ges `xN©w`b Ae ̄’vb Ki‡j gvby‡li i3Pvc †e‡o †h‡Z cv‡i| ZvB m1⁄2xZ ̧Y kã gvby‡li g‡b cÖkvwšÍ m„wó K‡i wbivc‡` iv‡L| M awi, P I Q myikjvKvi Zi1⁄2‣`N© ̈ h_vμ‡g P I Q P I Q myikjvKvi K¤úv1⁄4 h_vμ‡g fP I fQ  4P = 5 Q  P = 5 4 Q Avevi, fQ – fP = 60 [ P > Q]  fQ = 60 + fP ...... (i) GLv‡b, fP P = fQ Q  fP  5 4 Q = fQ  Q  fQ = 5 4 fP ......(ii) (i) I (ii) bs n‡Z, 5 4 fP = 60 + fP  5 fP = 240 + 4fP  fP = 240 Hz (ii)  fQ = 5 4  240 = 300 Hz AZGe, P I Q myikjvKvi K¤úv1⁄4 h_vμ‡g 240 Hz I 300 Hz| (Ans.) N †`Iqv Av‡Q, R myikjvKv Øviv m„ó AMÖMvgx Zi‡1⁄2i mgxKiY, Y = 0.2 sin 2    100t –  x 15  Y = 0.2 sin 2 15 (1500t – x) ...... (i) Avgiv Rvwb, AMÖMvgx Zi‡1⁄2i mgxKiY, Y = a sin 2  (vt – x) ...... (ii)