Q.14 The figure shows a snap photograph of a vibrating string at t = 0. The particle P is observed moving up with velocity 20 cm/s. The angle made by string with x-axis at P is 6º.
(a) Find the direction in which the wave is moving
(b) the equation of the wave
(c) the total energy carried by the wave per cycle of the string, assuming that µ, the mass per unit length of the string =
50 gm/m.
Attachments:
Answers
Answered by
1
Thus the total energy of the system is T.E = 1.6 x 10^-5 J
Explanation:
- Particle velocity
vp = −V (w) dy / dt ⇒ 20 √3 = −√3 V(w)
⇒|V(w)| = 20 cm/s
λ = 5.5 - 1.5 = 4 cm
K = 2 π / λ
=> π / 2 cm
A = 4 cm
V = ω / k => 20 = ω^2 / π
- Angular frequency ω = kv
= 50 π × 1 / 5 = 10π
Now at t = 0, x = 0
y = A sin(l)
2 √2 = 4 sin (l)
sin (l) = 1 / √2
l = π / 4 cm
(b) y = 0.4 sin ( π / 2 x 10^-2 x + 10 π + π / 4)
(c) T.E = 4 x 5 λ = 1/2 ρ A^2 ω^2 . s. λ
= 1 / 2 μ A^2 ω^2 . λ
= 1/2 x 50 x 10^-3 x (0.04)^2 (10π)^2 . 4 x 10^-2
= 1.6 x 10^-5 J
Thus the total energy of the system is T.E = 1.6 x 10^-5 J
Similar questions