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

Answer 2

The tension you must adjust the screw and the speed of the wave are;

A) Tension = 18.7 N

B) Speed = 29.14 m/s

Standing Waves

We are given;

Length of wire; L = 75 cm = 0.75 m

Mass of wire; m = 16.5 g = 0.0165 kg

A) Wavelength; λ = 3.33 cm = 0.0333 m

Frequency; f = 875

Formula for speed is;

v = fλ

Thus;

v = 875 × 0.0333

v = 29.14 m/s

In standing waves, we know that the speed relationship with the tension is; v = √(F/μ)

where;

• v = speed

• F = tension

• μ = linear density which is the mass per unit length

Thus; μ = m/L = 0.0165/0.75 = 0.022 kg/m

Making F the subject of the formula gives;

F = μv²

Thus; F = 0.022 × 29.14²

F ≈ 18.7 N

Read more on Standing waves at;  https://brainly.com/question/8460430