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## A wire with mass 90.0g is stretched so that its ends are tied down at points 88.0cm apart. The wire vibrates in its fundamental mode with fr

Question

A wire with mass 90.0g is stretched so that its ends are tied down at points 88.0cm apart. The wire vibrates in its fundamental mode with frequency 80.0Hz and with an amplitude of 0.600cm at the antinodes.a) What is the speed of propagation of transverse waves in the wire?b) Compute the tension in the wire.

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Physics
3 years
2021-08-24T14:36:36+00:00
2021-08-24T14:36:36+00:00 1 Answers
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## Answers ( )

Answer:a) V = 140.8 m/s

b) T = 2027.52 N = 2.03 KN

Explanation:a)The formula for the speed of the wave is given as follows:

f₁ = V/2LV = 2f₁Lwhere,

V = Speed of Wave = ?

f₁ = Fundamental Frequency = 80 Hz

L = Length of Wire = 88 cm = 0.88 m

Therefore,

V = (2)(80 Hz)(0.88 m)V = 140.8 m/sb)Another formula for the speed of wave is:

V = √T/μV² = T/μT = V²μwhere,

T = Tension in String = ?

μ = Linear Mass Density of Wire = Mass of Wire/L = 0.09 kg/0.88 m

μ = 0.1 kg/m

Therefore,

T = (140.8 m/s)²(0.1 kg/m)T = 2027.52 N = 2.03 KN