# Which Pulse Reaches the Knot First?

• logix24
In summary, the problem involves two strings with different linear densities and lengths, one under tension, and a pulse traveling towards the knot. The equations used to solve for the speed of the pulses are v=√(T_s/μ), with T_s representing the tension and μ representing the linear density. The pulse on string one is faster with a speed of 1690m/s compared to the pulse on string two with a speed of 1195m/s. The tension in each string must remain the same for the forces on the knot to cancel. The lengths of the strings are mentioned in the problem, but they are not directly used in the solution.
logix24

## Homework Statement

Two strings have been tied together with a knot and stretched between two rigit supports. The strings have linear densities µ1 = 1.4 x 10-4 kg/m and µ2 = 2.8 x 10-4 kg/m. Their lengths are L1 = 3.0m and L2 = 2.0m, and string one is under 400N tension. If a pulse is started simultaneously on each string, traveling towards the knot, which pulse reaches the knot first?

v=√(T_s/μ)

## The Attempt at a Solution

v1=√(400N/(1.4 x 10^-4 kg/m)=1690m/s)
v2=√(400N/(2.8 x 10^-4 kg/m)=1195m/s)

v1 should be faster, but I know that I'm missing something in my equations. We've been given the two lengths of the strings and the tension of only one string, so how do I utilize the value of the lengths in my formula?

Time=dist/v.
The knot doesn't move. What does that say about the tension in each strilng?

Does the tension remain the same in each string?

Yes, the two forces on the knot must cancel.

So then why does the question give the two lengths of the string and do I use the values of Length in solving the problem?

time=length divided by speed.

## What is the difference between v1 and v2 in the wave speed of strings?

V1 and v2 represent two different wave speeds in the context of strings. V1 is the speed of a wave on a string when the tension and mass per unit length are constant. V2 is the wave speed when the tension and mass per unit length are varied.

## How is the wave speed of a string affected by tension?

The wave speed of a string is directly proportional to the tension in the string. This means that as the tension increases, the wave speed also increases. Similarly, if the tension decreases, the wave speed will decrease.

## What is the relationship between wave speed and mass per unit length in a string?

The wave speed of a string is inversely proportional to the mass per unit length. This means that as the mass per unit length increases, the wave speed decreases, and vice versa.

## What factors can affect the wave speed of a string?

The wave speed of a string can be affected by several factors including tension, mass per unit length, temperature, and the material of the string. Changes in any of these factors can cause a change in the wave speed of the string.

## How is the wave speed of a string measured?

The wave speed of a string can be measured by dividing the wavelength of the wave by the period of the wave. This will give the frequency of the wave, which can then be used to calculate the wave speed using the equation v = fλ, where v is the wave speed, f is the frequency, and λ is the wavelength.

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