Answer: (a). Tension = 612.5 N
(b). Maximum transverse speed = 9.42m/s
acceleration of node and antinode = 2957.88 m/s²
(c). wavelength = 7m
Explanation:
ok to begin,
we would define the parameters given;
the length L = 2m
mass M = 10g = 10×10⁻³kg
frequency F = 50Hz
speed of sound V = 350 m/s
amplitude A = 3cm = 0.03m
(a). from formula;
V = √(T/μ) ................(1)
where μ = linear mass density which is given as
μ = m/L = 10⁻²/ 2 = 0.5×10⁻² kg/m
from equation 1,
V² = T/μ
T = V² × μ
T = 350²×0.5×10⁻²
T = 612.5 N
(b). to solve the for the maximum speed;
Vmax = AW
Vmax = A × 2πf
Vmax = 0.03 × 2π × 350
Vmax = 9.42m/s
(ii). the general form for the maximum transverse acceleration of the node and antinode is given as;
Am = W² × ym
= (2π50)² × 0.03
Am = 2957.9 m/s²
(c) wavelength of the sound is given;
V = Fλ
where λ = V/F
λ = 350/ 50
λ = 7m
