Question

A thin, 75.0 cm wire has a mass of 16.5 g. One end is tied to a nail, and the other is attached to a screw that can be adjusted to vary the tension in the wire. (a) To what tension in Newtons must you adjust the screw to that a transverse wave of wavelength 3.33 cm makes 875 vibrations per second? (b) How fast would this wave travel?

Answer 1

Answer:

(a) 29.14 m/s

(b) 18.7 N

Explanation:

given information:

L = 75 cm = 0.75 m

mass, m = 16.5 g = 1.65 x 10⁻² kg

wavelength, λ = 3.33 cm = 0.0333 m

frequency, f = 875

first we calculate the speed

v = λf

  = 0.0333 x 875

  = 29.14 m/s

v = √F/μ

where

v = speed

F = tension

μ = linear density

μ = m/L, m is mass, and L is the length

thus,

v² = F/(m/L)

F = v²m/L

  = (29.14)²(1.65 x 10⁻² )/(0.75)

  = 18.7 N