# What is the tension in the string?

• I_LuV_FiZiX
In summary, by setting the two given equations for the string's vibration frequency equal to each other and using the fact that the string vibrates at integer multiples of a fundamental frequency, we can solve for the tension in the string. The final answer is 2.77N.
I_LuV_FiZiX

## Homework Statement

A string from an Andrew Kirk violin is 30.0 cm long, with a linear density of 0.645 g/m. The violin is placed near a loudspeaker that is fed by an audio oscillator of variable frequency. It is found that the string is set into oscillation only at the frequencies 1312 Hz and 1749 Hz, as the frequency of the oscillator is varied over the range 1093 Hz to 1968 Hz. What is the tension in the string?

## Homework Equations

v=sqrt(T/linear density) v=lambda x frequency

## The Attempt at a Solution

I made these 2 equations equal to each other. However, I am unsure as to what proportion of L lambda is, and what to use for frequency. Once I know what to do here I can then isolate for tension and solve.

Thanks in advance, any help would be GREATLY appreciated.

can you give me a further hint as to how to find what to use for frequency? I've got less than an hour :S

The frequencies given will be integer multiples of a fundamental frequency. So 1312Hz will be $nf_1$ for example and 1749Hz will be the next integer multple from that, so it'll be $(n+1)f_1$.

oh okay...so is a final answer of correct? 2.77N I have one try left :S:S:S:S

Since length of the string remains the same, for different frequencies the number of loops must be different.
Hence 1312*(n+1) = 1749*n. Solve for n and then find tension.

## 1. What is tension?

Tension is a force that is exerted on an object, typically a string or rope, when it is pulled in opposite directions. It is also known as the force of stretch or strain.

## 2. How is tension measured?

Tension is measured in units of force, such as newtons (N) or pounds (lbs). It can also be measured using a tension meter or by calculating the force required to stretch a string.

## 3. What factors affect the tension in a string?

The tension in a string is affected by the force applied to it, the length and thickness of the string, and the material properties of the string such as elasticity and stiffness.

## 4. Why is tension important in science?

Tension plays a crucial role in many scientific fields, including physics, engineering, and biology. It helps us understand the behavior of objects under stress and is essential for designing structures and predicting the movement of objects.

## 5. How does tension affect the motion of an object?

Tension can either accelerate or decelerate an object, depending on the direction of the force and the mass of the object. If the tension force is greater than any opposing forces, the object will accelerate in the direction of the tension. If the tension force is less than opposing forces, the object will decelerate or come to a stop.

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