# Max speed of wave on a string from elastic limit given density

• lizzyb
In summary, the conversation discusses how to determine the maximum speed that transverse wave pulses can propagate along a piece of steel wire without exceeding the elastic limit of 2.7 X 10^9 Pa. The formula v = \sqrt{\frac{T}{\mu}} is used, where T represents the tension in the wire and \mu is the volume mass density. The force can be obtained from the elastic limit by dividing it by the cross-sectional area. This information is helpful in understanding the relationship between pressure, force, and speed in this scenario.
lizzyb
How do I set this up? "The elastic limit of a piece of steel wire is 2.7 X 10^9 Pa. What is the maximum speed at which transverse wave pulses can propagate along this wire before this stress is exceeded? (The density of steel is 7.86 X 10^3 kg/m^3)

I know $$v = \sqrt{\frac{T}{\mu}}$$ so I guess I'd solve for T? And how do I pull the force from the elastic limit without the area?

thanx!

lizzyb said:
How do I set this up? "The elastic limit of a piece of steel wire is 2.7 X 10^9 Pa. What is the maximum speed at which transverse wave pulses can propagate along this wire before this stress is exceeded? (The density of steel is 7.86 X 10^3 kg/m^3)

I know $$v = \sqrt{\frac{T}{\mu}}$$ so I guess I'd solve for T? And how do I pull the force from the elastic limit without the area?

thanx!
Hi.

Notice that $\rho = { mass \over length \times area}$ and $\mu = {mass \over length}$ so that $\rho = {\mu \over area}$ where, by "area" I mean the cross sectional area.

Also, Pressure = Force over area, so $P_{max} = {T_{max} \over area}$. With this you should be able to rewrite the speed in terms of the pressure and the volume mass density $\rho$.

I hope this helps

Patrick

yes it helped! i hope i remember it! thanks!

## 1. What is the maximum speed of a wave on a string from the elastic limit given density?

The maximum speed of a wave on a string is directly related to the string's density and the elastic limit. The formula for calculating the maximum speed is v = √(T/μ), where v is the maximum speed, T is the tension in the string, and μ is the linear mass density.

## 2. How does the elastic limit affect the maximum speed of a wave on a string?

The elastic limit is the maximum stress a material can withstand before it deforms permanently. In the context of a string, this means that the tension in the string cannot exceed the elastic limit without causing permanent damage. Therefore, the maximum speed of a wave on a string is limited by the elastic limit because it determines the maximum tension that can be applied.

## 3. Can the density of a string affect the maximum speed of a wave?

Yes, the density of a string has a direct impact on the maximum speed of a wave. A higher density string will have a lower maximum speed because it requires more energy to create waves due to its heavier mass. On the other hand, a lower density string will have a higher maximum speed because it requires less energy to create waves.

## 4. Is the maximum speed of a wave on a string affected by the length of the string?

No, the length of a string does not affect the maximum speed of a wave. This is because the maximum speed is determined by the tension and density of the string, not its length. However, the wavelength of the wave will be affected by the length of the string.

## 5. How can the maximum speed of a wave on a string be measured?

The maximum speed of a wave on a string can be measured using a variety of methods, such as using a stroboscope or a high-speed camera to capture the motion of the string. The speed can also be calculated using the formula v = √(T/μ), where T is the tension in the string and μ is the linear mass density.

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