The linear density of a vibrating string is 1 3×104kg/m A transverse wave is propagating on the string and - Science - Sound

Question

The linear density of a vibrating string is 1
3×104kg/m A transverse wave is propagating on the
string and is described by the equation y = 0 021 sin (30t + x),
where x, y are measured in m and t in s Find the tension in the
wire

Vara · Accepted Answer

General equation of progressive wave:

y=A sinωt+kxHere, A is amplitude ω is angular frequency
κ is propagation constant t is time x is displacement

Given equation:

y=0 021 sin30t+x

Compare with general equation:

A=0 021 mω = 30 rad/sκ = 1 m-1

Velocity of the wave in the string:

v=ωk =301 =30 m/s

Relation for velocity velocity in terms of tension:

v=TμHere, T is tension and μ is linear density

Expression for tension:

T=μv2 =1 3×10-4302 =0 12 N

The linear density of a vibrating string is 1.3×104kg/m. A transverse wave is propagating on the string and is described by the equation y = 0.021 sin (30t + x), where x, y are measured in m and t in s. Find the tension in the wire

The linear density of a vibrating string is 1.3×10⁴kg/m. A transverse wave is propagating on the string and is described by the equation y = 0.021 sin (30t + x), where x, y are measured in m and t in s. Find the tension in the wire