Content text 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 cÖkœ1 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 100t cos5x Y = 200 sin 100t cos5x Y = A sin 100t ; †hLv‡b, A = 200 cos5x m‡e©v”P we ̄Ív‡ii Ae ̄’v‡bi †ÿ‡Î, A = 200 m A_©vr, cos 5x = 1 5x = 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.) cÖkœ2 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|
2 .................................................................................................................................. HSC Physics 1 st Paper Chapter-9 Rhombus Publications M †`Iqv Av‡Q, GKwU Zi‡1⁄2i mgxKiY, y = 3 sin 36t + 0.018x + 4 ...... (i) Avgiv Rvwb, y = a sin (t + ) ...... (ii) (i) bs I (ii) bs mgxKiY Zzjbv K‡i cvB, = 36 2 T = 36 T = 2 36 = 0.175 s Zi1⁄2wUi ch©vqKvj, T = 0.175 s (Ans.) N †`Iqv Av‡Q, GKwU Zi‡1⁄2i mi‡Yi mgxKiY, y = 3 sin 36t + 0.018x + 4 x = 0 a‡i, y = 3 sin 36t + 4 v = dy dt = 36 3 cos 36t + 4 = 108 cos 36t + 4 v – t MÖv‡di cÖK...wZ wb¤œiƒc: 16 144 17 144 108 76.37 –108 myZivs, †eM ebvg mgq †jLwPÎ GKwU cosine †jLwPÎ n‡e Ges hvi Avw` `kv n‡e 4 | (Ans.) cÖkœ3 A, B, C Ges D PviwU myikjvKv †`qv Av‡Q, hvi g‡a ̈ A kjvKvwU 1.3 kgm –3 Nb‡Z¡i gva ̈‡g 0.5 m we ̄Ív‡ii kã Zi1⁄2 m„wó K‡i| kjvKvwUi K¤úv1⁄4 250 Hz Ges gva ̈‡g k‡ãi †eM 345 ms –1 | A kjvKvwU B Ges D Gi mv‡_ h_vμ‡g cÖwZ †m‡K‡Û 2wU Ges 6wU exU Drcbœ K‡i Ges B I D ci ̄ú‡ii mv‡_ cÖwZ †m‡K‡Û 4wU exU Drcbœ K‡i Ges B, D, C Gi mv‡_ `ywU exU Drcbœ K‡i| (K) w ̄’i Zi1⁄2 Kx? [h. †ev. 19] (L) Abybv`x e ̄‘i Dcw ̄’wZ gva ̈‡gi kã Zi‡1⁄2i ZxeaZvi Dci Kxfv‡e cÖfve we ̄Ívi K‡i e ̈vL ̈v Ki| [h. †ev. 19] (M) A myikjvKvi m„ó k‡ãi ZxeaZv wbY©q Ki| [h. †ev. 19] (N) ÒexU MYbv K‡i ARvbv myikjvKvi K¤úv1⁄4 wbY©q Kiv m¤¢eÓÑ C myikjvKvi K¤úv1⁄4 wbY©q K‡i Dw3wUi h_v_©Zv we‡kølY Ki| [h. †ev. 19; Abyiƒc Xv. †ev. 17] DËi: K †Kv‡bv gva ̈‡gi GKwU mxwgZ As‡k ci ̄úi wecixZgyLx mgvb we ̄Ívi I Zi1⁄2‣`‡N© ̈i `ywU AMÖMvgx Zi1⁄2 G‡K Ac‡ii Dci AvcwZZ n‡j †h bZzb Zi1⁄2 m„wó nq Zv‡K w ̄’i Zi1⁄2 e‡j| L k‡ãi ZxeaZv kã Zi‡1⁄2i we ̄Ív‡ii e‡M©i mgvbycvwZK (I a 2 )| ̄ú›`bÿg e ̄‘i Dci Av‡ivwcZ ch©ve„Ë ̄ú›`‡bi Rb ̈ e ̄‘wU Zvi ̄^vfvweK K¤úv‡1⁄4 Kw¤úZ nIqvi cwie‡Z© Av‡ivwcZ ev ciek K¤ú‡bi K¤úv‡1⁄4 Kw¤úZ n‡e| Abybv‡`i †ÿ‡Î Av‡ivwcZ ̄ú`‡bi K¤úv1⁄4 I e ̄‘i ̄^vfvweK K¤úv1⁄4 mgvb nIqvq we ̄Ívi me©vwaK nq| ZvB ejv hvq| Abybv`x e ̄‘i Dcw ̄’wZ K¤ú‡bi we ̄Ívi e„w×i ga ̈ w`‡q gva ̈‡g kã Zi‡1⁄2i ZxeaZv e„w× Ki‡e| M †`Iqv Av‡Q, gva ̈‡gi NbZ¡, = 1.3 kgm–3 we ̄Ívi, a = 0.5 m K¤úv1⁄4, f = 250 Hz k‡ãi †eM, v = 345 ms–1 k‡ãi ZxeaZv, I = ? Avgiv Rvwb, I = 2 2 f 2 a 2 v = 2 2 (250)2 (0.5)2 1.3 345 = 138328674.2 Wm–2 (Ans.) N †`Iqv Av‡Q, fA = 250 Hz fA fB = 2 fA fD = 6 fB fD = 4 fB fC = 2 fD fC = 2 B myikjvKvi K¤úv1⁄4 = 248 Hz A_ev 252 Hz D myikjvKvi K¤úv1⁄4 = 244 Hz A_ev 256 Hz C myikjvKvi K¤úv1⁄4 = 242 Hz, 246 Hz, 250 Hz, 254 Hz A_ev 258 Hz GLv‡b, C myikjvKvi K¤úv1⁄4 †KejgvÎ 246 Hz A_ev 254 Hz n‡j Zv mKj kZ© †g‡b P‡j| AZGe, C myikjvKvi K¤úv1⁄4 = 246 Hz A_ev 254 Hz myZivs, ÒexU MYbv K‡i ARvbv myikjvKvi K¤úv1⁄4 wbY©q Kiv m¤¢e|Ó Dw3wU h_v_©| (Ans.) cÖkœ4 wb‡Pi wP‡Î †Kv‡bv GK cixÿvMv‡i `ywU myikjvKv A I B †K kãvwqZ Ki‡j †h Zi1⁄2 Drcbœ nq Zvi †jLwPÎ †`Lv‡bv n‡jv: 3.2 m TA = 0.01 s 3.2 m wPÎ : A kjvKv wbtm„Z Zi1⁄2 wPÎ : B kjvKv wbtm„Z Zi1⁄2 (K) msmw3 ej Kx? [Kz. †ev. 19] (L) GKwU †gvUv I GKwU wPKb B ̄úv‡Zi Zv‡ii Bqs Gi ̧bv1⁄4 mgvb n‡e wK-bv e ̈vL ̈v Ki| [Kz. †ev. 19] (M) cixÿvMv‡i A kjvKvi Øviv m„ó k‡ãi †eM KZ wbY©q Ki| [Kz. †ev. 19; Abyiƒc w`. †ev. 17] (N) DÏxc‡Ki myikjvKv `ywU GK‡Î evRv‡j exU Drcbœ Ki‡e wKbv Zv MvwYwZKfv‡e e ̈vL ̈v Ki| [Kz. †ev. 19; Abyiƒc iv. †ev. 16]
4 .................................................................................................................................. HSC Physics 1 st Paper Chapter-9 Rhombus Publications (i) I (ii) bs Zzjbv K‡i cvB, we ̄Ívi, a = 0.2 m Zi1⁄2‣`N© ̈, = 15 m Zi1⁄2‡eM, v = 1500 ms–1 Zi‡1⁄2i K¤úv1⁄4, f = v = 1500 15 = 100 Hz GLv‡b, R myikjvKv Øviv m„ó AMÖMvgx Zi1⁄2 abvZ¥K X-Aÿ eivei MwZkxj| Avevi, ci ̄úi wecixZgyLx mgvb we ̄Ívi I Zi1⁄2‣`N© ̈i `ywU AMÖMvgx Zi1⁄2 G‡K Ac‡ii Dci AvcwZZ n‡j w ̄’i Zi1⁄2 m„wó nq| ZvB ejv hvq, 0.2 m we ̄Ívi, 15 m Zi1⁄2‣`N© ̈ Ges 100 Hz K¤úv1⁄4 wewkó GKwU AMÖMvgx Zi1⁄2 wecixZgyLx A_©vr, FbvZ¥K X- Aÿ eivei Pvjbv Kiv‡j R myikjvKvi Zi1⁄2 Øviv w ̄’i Zi1⁄2 cvIqv hv‡e| (Ans.) cÖkœ6 GKwU †cvwëadv‡g© 400 gyiwM Av‡Q| †cvwëadv‡g©i eZ©gvb k‡ãi ZxeaZv 3.2 10–4 Wm–2 | †cvwëadv‡g©i gvwjK gyiwMi msL ̈v evwo‡q 2400 wU Ki‡jb| [k‡ãi cÖgvY ZxeaZv 10–12 Wm–2 ] (K) kã Kv‡K e‡j? [wm. †ev. 19] (L) Zx2Zv I K¤úv1⁄4 GKB wK bv? e ̈vL ̈v Ki| [wm. †ev. 19] (M) DÏxc‡Ki †cvwëadv‡g©i ZxeaZv †j‡fj KZ †ej wQj wbY©q Ki| [wm. †ev. 19] (N) gyiwMi msL ̈v evov‡bvi d‡j DÏxc‡Ki dvg©wU‡Z Kx ai‡bi mgm ̈vi m„wó n‡Z cv‡i? MvwYwZKfv‡e e ̈vL ̈v Ki| [wm. †ev. 19; Abyiƒc h. †ev. 17] DËi: K †h kw3 †Kv‡bv K¤úbkxj e ̄‘ †_‡K Drcbœ n‡q Awew”Qbœ I w ̄’wZ ̄’vcK gva ̈‡gi ga ̈w`‡q mÂvwjZ n‡q Avgv‡`i Kv‡b †cu.Qvq Ges kÖe‡Yi Abyf~wZ m„wó K‡i Zv‡K kã e‡j| L k‡ãi †h •ewkó ̈ Øviv †Kvb myi miæ I †Kvb myi †gvUv Zv †evSv hvq Zv‡K Zx2Zv ev wcP e‡j| Avi †Kvb GKwU K¤úgvb e ̄‘ GK †m‡K‡Û hZ msL ̈K c~Y© †`vjb m¤úbœ K‡i, Zv‡K D3 e ̄‘i K¤úv1⁄4 e‡j| miæ ev Pov my‡ii K¤úv1⁄4 †ewk, ZvB Gi Zx2ZvI †ewk| †Zgwb †gvUv ev Lv‡`i my‡ii K¤úv1⁄4 Kg, ZvB Gi Zx2ZvI Kg| †Kv‡bv ̄^‡ii Zx2Zv ej‡Z H ̄^‡ii AšÍM©Z g~jmy‡ii Zx2Zv †evSvq| ZvB ejv hvq, K¤úv‡1⁄4i mv‡_ Zx2Zvi m¤úK© _vK‡jI Giv GK bq| M †`Iqv Av‡Q, k‡ãi ZxeaZv, I = 3.2 10–4 Wm –2 k‡ãi cÖgvY ZxeaZv , I0 = 10–12 Wm –2 Avgiv Rvwb, ZxeaZv †j‡fj, = log I I0 = log 3.2 10–4 10–12 = 8.5 B (Ans.) N GLv‡b, bZzb k‡ãi ZxeaZv, I' = 2400 400 3.2 10–4 = 1.92 10–3 Wm –2 k‡ãi cÖgvY ZxeaZv , I0 = 10–12 Wm –2 Avgiv Rvwb, bZzb ZxeaZv †j‡fj, ' = 10 log I' I0 = l0 log 1.92 10–3 10– 12 = 92. 83 dB AZGe, gyiwMi msL ̈v evov‡bvi d‡j DÏxc‡Ki dvg©wU‡Z k‡ãi ZxeaZv †j‡fj †e‡o wM‡q 92.83 dB n‡e| †hLv‡b `xN© mgq _vK‡j Zv ̄^v‡ ̄’ ̈i c‡ÿ ÿwZKviK| (Ans.) cÖkœ7 A I B Zvi‡K Kw¤úZ K‡i wb‡¤œi Zi1⁄2Øq Drcbœ nq: YA = 0.1 sin (200 t – 10 x) m YB = 0.1 sin (208 t – 16 x) m Zi1⁄2Øq GKBw`‡K Mgb K‡i ci ̄úi DcwicvwZZ nq| (K) FYvZ¥K KvR Kx? [e. †ev. 19] (L) M ̈v‡mi NbZ¡ †ewk n‡j Mogy3 c_ †ewk nq wK? e ̈vL ̈v Ki| [e. †ev. 19] (M) A Zv‡i m„ó Zi‡1⁄2i Zi1⁄2‡eM wbY©q Ki| [e. †ev. 19; Abyiƒc Kz. †ev. 17] (N) DÏxc‡Ki Zvi؇qi K¤ú‡b exU m„wó m¤¢e wK bv MvwYwZK ZË¡mn gZvgZ `vI| [e. †ev. 19; Abyiƒc h. †ev. 17] DËi: K ej cÖ‡qv‡Mi d‡j hw` e‡ji cÖ‡qvM we›`y e‡ji wμqvi wecixZ w`‡K m‡i hvq ev e‡ji w`‡K mi‡Yi FYvZ¥K Dcvsk _v‡K Z‡e †h KvR m¤úvw`Z nq Zv‡K FYvZ¥K KvR e‡j| L cici `ywU av°vi wfZi AYy ̧‡jv M‡o mij‡iLvq hZUzKz c_ Mgb K‡i Zv‡K Mo gy3c_ e‡j| Avgiv Rvwb, Mogy3 c_, 1 | A_©vr, Mo gy3 c_ M ̈v‡mi Nb‡Z¡i e ̈ ̄ÍvbycvwZK| d‡j M ̈v‡mi NbZ¡ †ewk n‡j Mo gy3 c_ n«vm cv‡e| M †`Iqv Av‡Q, A Zv‡ii Zi1⁄2, YA = 0.1 sin (200 t – 10 x) YA = 0.1 sin 10 (20t – x) YA = 0.1 sin 2 1 5 (20t – x) ...... (i) Avgiv Rvwb, Y = a sin 2 (vt – x) ...... (ii) (i) bs I (ii) bs mgxKiY Zzjbv K‡i cvB, v = 20 ms–1 A Zv‡i m„ó Zi‡1⁄2i Zi‡1⁄2‡eM, v = 20ms–1 | (Ans.)