# Snapshot and history graphs for a string under tension (drive mechanism)

In summary, a string with mass density of 9.00 g/m, under tension of 25 N and driven by a mechanism at x = 0, has a velocity that varies with time according to vy(t) = 0 (if t = 0), 10.0 cm/s (if 0 < t ≤ 0.1 s), −20.0 cm/s (if 0.1 s < t ≤ 0.2 s), 10.0 cm/s (if 0.2 s < t ≤ 0.3 s), and 0 if t > 0.3 s. The wave speed can be calculated using the equation v = sqrt(T/u), but the value of

## Homework Statement

A string with mass density u = 9.00 g/m extends from zero to infinity along the x-axis. It is
under tension T = 25 N, and is driven by a mechanism at x = 0.

The velocity of the drive mechanism depends on time as:
vy(t) =
0 (if t = 0)
10.0 cm/s (if 0 < t ≤ 0.1 s)
−20.0 cm/s (if 0.1 s < t ≤ 0.2 s)
10.0 cm/s (if 0.2 s < t ≤ 0.3 s)
0 if t > 0.3 s

(a) Sketch a “snapshot graph” of the displacement of the string at time t = 0.5 s, from 0
to 30 m along the x-axis. Use a range of -1.0 cm to +1.0 cm on the y-axis.

(b) Sketch the “history graph” at x = 10 m, for t = 0 to 0.6 s.

## Homework Equations

v = sqrt(T/u)
Y = Yo cos(kx - w t)

## The Attempt at a Solution

I can calculate the wave speed from square root of (T/u)

a) t = 0.5 s
Therefore, vy(t) = -20.0 cm/s
At x = 0,
yo = -20.0 * 0.5 = -10.0 cm
But I do not know how y will vary with x. I thought of using
Y = yo cos(k x), where k is wave-number.
But do not know how to calculate the value of k as I do not know how to find wavelength or frequency.

b) x = 10 m
How do I find vy(t) at this value of x ?

I realized the graphs will not be sinusoidal. They will have straight lines. I have made history graph at x = 0
I calculated v = 52.7 m/s

How to draw snapshot graph at t = 0.5 s and history graph at x = 10 m ?

Snapshot is to be drawn at t = 0.5
vy(t) = 0 at t = 0.5

So can we say that the snapshot graph at t = 0.5 will be a single straight line coinciding with x axis?

## What is a snapshot graph for a string under tension?

A snapshot graph for a string under tension is a visual representation of the displacement of the string at a specific point in time. It shows the shape of the string as it is being pulled or stretched, and can also indicate the direction and magnitude of the tension force acting on the string.

## What is a history graph for a string under tension?

A history graph for a string under tension is a visual representation of the displacement of the string over a period of time. It shows how the string changes shape as it is being pulled or stretched, and can also show the relationship between the tension force and the displacement of the string.

## How are snapshot and history graphs used in studying string tension?

Snapshot and history graphs are used in studying string tension to analyze the behavior of the string under different tensions and to observe any patterns or changes over time. These graphs can also be used to make predictions about the behavior of the string under different conditions.

## What factors can affect the shape of a string in a snapshot graph?

The shape of a string in a snapshot graph can be affected by the magnitude of the tension force acting on the string, the length of the string, and the material properties of the string such as elasticity and stiffness. External factors such as temperature and humidity can also play a role in the shape of the string.

## How can snapshot and history graphs be used in real-world applications?

Snapshot and history graphs for a string under tension are commonly used in engineering and physics to study the behavior of strings in various systems, such as musical instruments, pulley systems, and suspension bridges. They can also be used in sports to analyze the movement of strings in equipment like tennis rackets and archery bows.

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