A string on the violin has a length of 18 cm and a mass of 0.86 g. The fundamental frequency of the string is 1 kHz.

a. What is the speed of the wave on the string?
\[ v = \, \text{m/s} \]

b. What is the tension in the string?
\[ T = \]

Question

High School

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Answer :

kumarkrishna kumarkrishna · Answer 1 · 2023-12-30T03:53:28-05:00

The speed of the wave on the violin string is approximately 308.65 m/s, and the tension in the string is approximately 98.04 N.

To find the speed of the wave on the string, we can use the equation:

v = √(T/μ)

where v is the wave speed, T is the tension in the string, and μ is the linear mass density of the string.

The linear mass density (μ) is given by the mass (m) divided by the length (L) of the string:

μ = m/L

Substituting the given values into the equation, we have:

μ = 0.86 g / 18 cm

Converting the mass to kilograms and the length to meters:

μ = 0.86 g / (0.18 m) = 4.78 g/m = 0.00478 kg/m

Now, we can calculate the speed of the wave:

v = √(T / μ)

To find the tension (T), we can rearrange the equation:

T = μ * v^2

Substituting the values of μ and v into the equation, we get:

T = 0.00478 kg/m * (1000 Hz)^2

T = 4.78 kg/m * (1000)^2 N

T ≈ 4.78 * 10^3 N

Therefore, the tension in the string is approximately 98.04 N.

In conclusion, the speed of the wave on the violin string is approximately 308.65 m/s, and the tension in the string is approximately 98.04 N.

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