āϏā§āϤā§āϰ :
āϏāĻŽā§āĻāϰâāĻŖ |
āĻĒā§āϰāϤā§āĻ āĻĒāϰāĻŋāĻāĻŋāϤāĻŋ āĻ āĻāĻāĻ |
ā§§.āĻāĻŽā§āĻĒāĻžāĻā§āĻ āĻ āĻĒāϰā§āϝāĻžā§āĻāĻžāϞā§āϰ āĻŽāϧā§āϝ⧠āϏāϰā§āĻŽā§āĻĒāĻ :n = 1/T ⧍.āϤāϰāĻā§āĻ āĻŦā§āĻ :v =nÎģ ā§Š.āϤāϰāĻā§āĻ āĻĻā§āϰā§āĻā§āϝ :Îģ = vT ā§Ē.āĻā§āĻŖāĻŋāĻ āĻāĻŽā§āĻĒāĻžāĻā§āĻ:Ī = 2Ī/T = 2Īn ā§Ģ.āĻāĻŽā§āĻĒāύāĻļā§āϞ āĻāĻŖāĻžāϰ āĻŦāĻžāϰ āĻāĻŽā§āĻĒāύ⧠āϤāϰāĻā§āĻ āĻāϰā§āϤā§āĻ āĻ āϤāĻŋāĻā§āϰāĻžāύā§āϤ āĻĻā§āϰāϤā§āĻŦ:S = NÎģ ā§Ŧ.āĻ āĻā§āϰāĻāĻžāĻŽā§ āϤāϰāĻā§āĻā§ āϏāĻŽā§āĻāϰāĻŖ : y=asin2ĪÎģ(vtâx) ā§.āϏā§āĻĨāĻŋāϰ āϤāϰāĻā§āĻā§āϰ āϏāĻŽā§āĻāϰāĻŖ : y=2acos2ĪxÎģsin2ĪvtÎģ=Asin2ĪvtÎģ ā§Ž.āϤāϰāĻā§āĻ āĻĒā§āϰāĻŦāĻžāĻšā§āϰ āĻāύā§āϝ āĻāĻāĻ āĻā§āϤāύā§āϰ āĻŽā§āĻ āĻļāĻā§āϤāĻŋ : E = 2Ī2Īn2a2 ⧝.āĻĻā§āĻāĻŋ āĻŽāĻžāϧā§āϝāĻŽā§ : VAVB=ÎģAÎģB
āĻāĻāĻ āĻŽāĻžāϧā§āϝāĻŽā§ : V1V2=Îģ1Îģ2=n2n1
ā§§ā§Ļ.āĻĻāĻļāĻž āĻĒāĻžāϰā§āĻĨāĻā§āϝ, δ=2ĪÎģà x āĻĒāĻĨ āĻĒāĻžāϰā§āĻĨāĻā§āϝ |
T = āĻĻā§āϞāύ āĻāĻžāϞ (s) n = āĻāĻŽā§āĻĒāĻžāĻā§āĻ (Hz) Îģ = āϤāϰāĻā§āĻ āĻĻā§āϰā§āĻā§āϝ (m) Ī = āĻā§āĻŖāĻŋāĻ āĻāĻŽā§āĻĒāĻžāĻā§āĻ (rads-1) N = āĻĒā§āϰā§āĻŖ āĻāĻŽā§āĻĒāύā§āϰ āϏāĻāĻā§āϝāĻž S = āĻĻā§āϰāϤā§āĻŦ (m) y = āϏāϰāĻŖ(m) a = āĻŦāĻŋāϏā§āϤāĻžāϰ (m) x = āϏāϰāĻŖ(m) v = āϤāϰāĻā§āĻ āĻŦā§āĻ (ms-1) t = āϏāĻŽā§ (s) Ī = āϏāĻŽāĻā§āĻŖāĻŋāĻ āĻŦā§āĻ(ms-1) Ī = āĻŽāĻžāϧā§āϝāĻŽā§āϰ āĻĻā§āϰāϤā§āĻŦ (Kgm3) E = āĻŽā§āĻ āĻļāĻā§āϤāĻŋ (J)
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āĻāĻžāĻŖāĻŋāϤāĻŋāĻ āϏāĻŽāϏā§āϝāĻž āĻ āϏāĻŽāĻžāϧāĻžāύāĻ
ā§§. 224Hz āĻāĻŽā§āĻĒāĻžāĻāĻ āĻŦāĻŋāĻļāĻŋāώā§āĻ āĻāĻāĻāĻŋ āϏā§āϰ āĻļāϞāĻžāĻāĻž āĻšāϤ⧠āĻāϤāĻĒāύā§āύ āĻļāĻŦā§āĻĻ āĻŦāĻžāϤāĻžāϏ⧠3sec āĻ 1008m āĻĻā§āϰāϤā§āĻŦ āĻ āϤāĻŋāĻā§āϰāĻŽ āĻāϰ⧠āĨ¤ āϤāϰāĻā§āĻ āĻĻā§āϰā§āĻā§āϝ āĻŦā§āϰ āĻāϰ āĨ¤
āϏāĻŽāĻžāϧāĻžāύ :
S = vt = nÎģt S = 1008m
âš Îģ = S/nt t = 3s
= 1008/(224Ã3) n = 224Hz
â´ S = 1.5m [ans]
⧍. āĻŦāĻžāϤāĻžāϏ⧠āĻļāĻŦā§āĻĻā§āϰ āĻŦā§āĻ 332ms-1 āĨ¤ 664Hz āĻāĻŽā§āĻĒāĻžāĻāĻā§āϰ āϏā§āϰ āĻļāϞāĻžāĻāĻžāĻā§ āĻŦāĻžāĻāĻžāϞ⧠100 āĻŦāĻžāϰ āĻāĻŽā§āĻĒāύ āĻāĻžāϞ⧠āĻāϤ āĻĻā§āϰāϤā§āĻŦ āĻ āϤāĻŋāĻā§āϰāĻŽ āĻāϰāĻŦā§ āĨ¤
āϏāĻŽāĻžāϧāĻžāύ :
S = NÎģ n = 664Hz
= N(v/n) v = 332 ms-1
= 100Ã(332/664) N = 100
â´ S = 50m [ans]
ā§Š. āϤāϰāĻā§āĻāϏā§āĻĨāĻŋāϤ 0.297m āĻŦā§āϝāĻŦāϧāĻžāύ⧠āĻ āĻŦāϏā§āĻĨāĻŋāϤ āĻĻā§āĻāĻŋ āĻāύāĻžāϰ āĻŽāϧā§āϝ⧠āĻĻāĻļāĻž āĻĒāĻžāϰā§āĻĨāĻā§āϝ 1.57 āϰā§āĻĄāĻŋā§āĻžāύ āĨ¤ āϤāϰāĻā§āĻ āĻā§āϏā§āϰ āĻāĻŽā§āĻĒāĻžāĻā§āĻ 280Hz āĻšāϞ⧠āϤāϰāĻā§āĻ āĻŦā§āĻ āĻāϤ?
āϏāĻŽāĻžāϧāĻžāύ :
θ = (2Īx)/Îģ n = 280Hz
âš Îģ = (2Īx)/θ x = .297m
âš Îģ = (2ĪÃ.297)/1.57 = 1.188m θ = 1.57rad
â´ v = nÎą = 280Ã1.188
â´ v = 332.6ms-1 [ans]
ā§Ē. āĻāĻāĻāĻŋ āϏā§āϰāĻļāϞāĻžāĻāĻžāϰ āĻŦāĻžāĻšā§āĻĻā§āĻŦā§ āϝ⧠āϏāĻŽā§ā§ 200 āĻŦāĻžāϰ āĻāĻŽā§āĻĒāύ āϏāĻŽā§āĻĒāύā§āύ āĻāϰā§,āϏ⧠āϏāĻŽā§ā§ āĻāĻāĻŋ āĻĻā§āĻŦāĻžāϰāĻž āϏā§āώā§āĻāĻŋ āĻļāĻŦā§āĻĻ āϤāϰāĻā§āĻ āĻŦāĻžāϤāĻžāϏ⧠140m āĻĻā§āϰāϤā§āĻŦ āĻ āϤāĻŋāĻā§āϰāĻŽ āĻāϰ⧠āĨ¤ āĻļāϞāĻžāĻāĻžāĻāĻŋāϰ āĻāĻŽā§āĻĒāĻžāĻā§āĻ 490Hz āĻšāϞ⧠āĻŦāĻžāϤāĻžāϏā§āϰ āĻŽāϧā§āϝ⧠āĻļāĻŦā§āĻĻā§āϰ āĻŦā§āĻ āύāĻŋāϰā§āύ⧠āĻāϰ āĨ¤
āϏāĻŽāĻžāϧāĻžāύ :
v = nÎģ = n(S/N) n = 490Hz
âš v = 490Ã(140/200) S = 140m
â´ v = 343ms-1 [ans] N = 200
ā§Ģ. Y = 10 sin2(t/0.02 â x/15) āϏāĻŽā§āĻāϰāĻŖāĻāĻŋ āĻāĻāĻāĻŋ āĻ āĻā§āϰāĻāĻžāĻŽā§ āϤāϰāĻā§āĻ āĻĒā§āϰāĻāĻžāĻļ āĻāϰ⧠āĨ¤ āĻĻā§āϰā§āĻā§āϝāϰ āĻāĻāĻ cm āĻ āϏāĻŽā§ā§āϰ sec āĨ¤ āϤāϰāĻā§āĻā§āϰ āĻŦāĻŋāϏā§āϤāĻžāϰ, āĻāĻŽā§āĻĒāĻžāĻā§āĻ, āϤāϰāĻā§āĻ āĻĻā§āϰā§āĻā§āϝ āĻāĻŦāĻ āϤāϰāĻā§āĻā§āϰ āĻŦā§āĻ āύāĻŋāϰā§āĻŖā§ āĻāϰ āĨ¤
āϏāĻŽāĻžāϧāĻžāύ :
y = 10 sin2(t/0.02 â x/15)
âš y = 10 sin2(5ot - x/15)
= 10 sin(2Ī/15)(750t-x)...(i)
we know,
y = a sin(2Ī/Îą)(vt-x)...(ii)
from equation (i) & (ii) âš
āĻŦāĻŋāϏā§āϤāĻžāϰ, a = 10cm [ans]
āϤāϰāĻā§āĻ āĻĻā§āϰā§āĻā§āϝ, Îģ = 15cm [ans]
āĻŦā§āĻ, v = 750mcs-1 [ans]
āĻāĻŽā§āĻĒāĻžāĻā§āĻ, n = v/Îģ = 750/15 = 50Hz [ans]