A transverse wave is traveling on a string. The displacement y of a particle from its equilibrium position is given by y = (0.021 m)sin(29t - 2x). Note that the phase angle (29t - 2.0x) is in radians, t is in seconds, and x is in meters. The linear density of the string is 1.80 10-2 kg/m. What is the tension in the string?
Physics · High School · Tue Nov 03 2020
Answered on
Answer: 3.7845 N
Explanation: The wave equation is given by
y = 0.021 sin (29t - 2x)
By comparing this to the general equation of a wave, we have that
y = A sin (ωt - kx)
Where ω = angular frequency.
After comparing, we see that
A = 0.021m, ωt = 29t and - 2x = - kx
Hence ω = 29 rad/s and k = 2.
The velocity of a wave is in relationship with angular frequency and wavenumber is given as
ω = kv
Where k = wave number
By substituting the parameters, we have that
29 = 2v
v = 29/2 = 14.5 m/s.
The velocity of wave in a spring is calculated using the formulae below.
v = √(T/u)
Where v = linear velocity = 14.5 m/s
T = tension =?
u = linear density = 1.80×10^-2 kg/m
By substituting the parameters, we have that
14.5 = √(T/ 1.80×10^-2)
By squaring both sides, we have that
14.5² = T/ 1.80×10^-2
T = 14.5² × 1.80×10^-2
T = 210.25 × 1.80×10^-2
T = 3.7845 N