Question

With what tension must a rope with length 2.70 m and mass 0.170 kg be stretched for transverse waves of frequency 43.0 Hz to have a wavelength of 0.810 m ?

Answer 1

Relation between wave speed and tension in rope is given by:

V = sqrt (T/)

= mass per unit length = m/L

T = Tension in rope

V = wave speed = frequency*wavelength

V = f*

So,

f* = sqrt (T/)

T = *f^2*^2

Given values are:

f = 43.0 Hz

= 0.810 m

= m/l = 0.170/2.70 kg/m

So,

T = Tension in rope = ?

T = (0.170/2.70)*(43.0*0.810)^2

T = 76.38 N

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