High School

Find the speed of waves on a violin string with a mass of 599 mg and a length of 20.8 m.

Answer :

The speed of waves on the violin string is approximately 14.04 m/s.

To find the speed of waves on a violin string, we can use the formula for wave speed on a string:

[tex]\[ v = \sqrt{\frac{T}{\mu}} \][/tex]

where:

  • v is the speed of waves on the string,
  • T is the tension in the string,
  • μ is the linear mass density of the string.

Given:

  • Mass of the string (m) = 599 mg = 0.599 g = 0.000599 kg
  • Length of the string (L) = 20.8 m

First, we need to calculate the linear mass density (\( \mu \)) of the string, which is given by:

μ = m/L

μ = 0.000599 / 20.8

μ = 2.88 × 10⁻⁵ kg/m

Next, we need to determine the tension in the string. The tension in the string can be calculated using the formula:

T = μ . g . L

where:

g is the acceleration due to gravity (approximately 9.81 m/s²).

T = 2.88 × 10⁻⁵ . 9.81 . 20.8

T = 0.00568 N

Now, we can calculate the speed of waves on the violin string using the formula:

v = [tex]\sqrt{\frac{T}{\mu}}[/tex]

v [tex]= \sqrt{\frac{0.00568}{2.88 \times 10^{-5}}[/tex]

v = √197.22

v ≈ 14.04 m/s

Therefore, the speed of waves on the violin string is approximately 14.04 m/s.