A string of linear mass density 4 g/cm is Vibrating
according to equation:-
y = A sin(1 20πt)cos(2π/5x)
where x is in centimeters.
Find the tension in the string
(1) 3.6 N
(2) 36 N
(3) 7.2 N
(4) 72 N
Answers
answer : option (1) 3.6 N
it is given that a string of linear mass density, μ = 4g/cm = 4 × 10^-3/10^-2 kg/m = 0.4 kg/m
equation of vibrating equation, y = Asin(120 πt)cos(2π/5 x)
here ω = 120π and k = 2π/5
velocity of sound, v = ω/k
= (120π)/(2π/5)
= 300 cm/s = 3 m/s
tension in the string, v = √{T/μ}
⇒v² = T/μ
⇒(3)² = T/(0.4)
⇒T = 9 × 0.4 = 3.6 N
hence tension in the string is 3.6 N
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equation of vibrating equation, y = Asin(120 πt)cos(2π/5 x)
here ω = 120π and k = 2π/5
velocity of sound, v = ω/k
= (120π)/(2π/5)
= 300 cm/s = 3 m/s
tension in the string, v = √{T/μ}
⇒v² = T/μ
⇒(3)² = T/(0.4)
⇒T = 9 × 0.4 = 3.6 N