Question

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(25t - 2.0x). Note that the phase angle 25t - 2.0x is in radians, t is in seconds, and x is in meters. The linear density of the string is 2.3 × 10^-2 kg/m. What is the tension in the string?

Answer 1

We know that speed of transverse wave is given by:

V = sqrt (T/)

= mass per unit length = m/L = 2.3*10^-2 kg/m

T = tension in string = ?

V = wave speed = w/k

from given transverse wave equation:

y = 0.021*sin (25t - 2.0 x)

Compare it with standard wave equation:

y = A*sin (wt - kx)

k = wave number = 2.0 per m

w = angular frequency = 25 per sec

So, V = sqrt (T/)

T = *V^2 = *(w/k)^2

T = 2.3*10^-2*(25/2.0)^2

T = 3.59375 N

In two significant figures:

T = 3.6 N

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