# Caculating the tention, max accaleration and velocity of a violin string

• mmoadi
In summary, the string on the violin is made of steel wire with a diameter of 0.25 mm. To achieve a basic frequency of 660 Hz, the string must be strained with a force of 73.61 N. The maximum velocity of the string is 429 m/s and the maximum acceleration is 85897 m/s² when evoking basic vibration with an amplitude of 5 mm. The string has a volume of 16 x 10^-9 m³ and a mass of 0.00013 kg, resulting in a linear mass density of 0.0004 kg/m.
mmoadi

## Homework Statement

String on the violin is made of steel wire with a diameter of 0.25 mm. With what force must the string be strained (stretched) so that its basic frequency will equal 660 Hz (E-string)? What is the maximum velocity and acceleration of the parts of the string, if we evoke basic vibration with amplitude of 5 mm? In the rest, the fastened string is long l = 325 mm, the density of steel is 7800 kg/m3.

μ= m/L
v= 2Lf
a(max)= ω²A

## The Attempt at a Solution

First part: With what force must the string be strained so that its basic frequency will equal 660 Hz (E-string)?

Volume of cylinder: V= πr²h= π(1/d)²L= 16 x 10^-9 m³, ρ= 7800 kg/m³
Mass of the string: m= Vρ= 0.00013 kg
Linear mass density: μ= m/L (kg/m)→ μ= 0.0004 kg/m

v= 2Lf= 2(0.325m)(660 hz)= 429 m/s
v= sqrt(T/ μ) → T or F= μv²
F= 73.61 N

Second part: What is the maximum velocity and acceleration of the parts of the string, if we evoke basic vibration with amplitude of 5 mm?

v= 2Lf= 2(0.325m)(660 hz)= 429 m/s
a(max)= ω²A= (2πf)²A= 85897m/s²

Looks right to me.

Thank you.

## 1. How do you calculate the tension of a violin string?

The tension of a violin string can be calculated using the formula T = (m*L*f)^2, where T is the tension, m is the mass per unit length of the string, L is the length of the string, and f is the frequency of the string. This formula takes into account the weight and length of the string, as well as the frequency at which it vibrates.

## 2. What is the maximum acceleration of a violin string?

The maximum acceleration of a violin string can be calculated using the formula a = (4*pi^2*f^2)*A, where a is the maximum acceleration, f is the frequency of the string, and A is the amplitude of the string's vibration. This formula takes into account the frequency and amplitude of the string's vibration, which determine the maximum acceleration it can achieve.

## 3. How do you calculate the velocity of a violin string?

The velocity of a violin string can be calculated using the formula v = 2*pi*f*A, where v is the velocity, f is the frequency of the string, and A is the amplitude of the string's vibration. This formula takes into account the frequency and amplitude of the string's vibration, which determine the velocity at which it moves.

## 4. What factors affect the tension of a violin string?

The tension of a violin string is primarily affected by its mass per unit length, its length, and the frequency at which it vibrates. Other factors that can affect tension include temperature, humidity, and the material of the string.

## 5. How does the tension of a violin string affect its sound?

The tension of a violin string is directly related to the pitch it produces. Higher tension results in a higher pitch, while lower tension results in a lower pitch. Additionally, the tension also affects the tone and quality of the sound produced by the string. A well-tuned and properly tensioned string will produce a clear, resonant sound, while an improperly tensioned string can sound dull or out of tune.

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