# How Long Does a Point on a String Take to Move Between +2.0mm and -2.0mm?

• Sdawg1969
In summary, the conversation discusses finding the time it takes for a given point on a string to move between displacements of +2.0mm and -2.0mm, given the wave equation y(x,t)=(6.0mm)sin(kx+(600rad/s)t+\Phi). The individual attempts to solve the problem and discusses assumptions and calculations, and eventually comes to a solution of \Deltat = 0.00113s.
Sdawg1969

## Homework Statement

If y(x,t)=(6.0mm)sin(kx+(600rad/s)t+$$\Phi$$) describes a wave traveling along a string, how much time does any given point on the string take to move between displacements y= +2.0mm and y= -2.0mm?

## Homework Equations

I think y(t)=ym sin($$\omega$$t) ?

## The Attempt at a Solution

well if I plug in 2.0mm for y, 6.00mm for ym and 600rad/s for $$\omega$$ I come up with the equation 2.0mm=6.00mm sin (600rad/s * t). Where do I go from here? are my assumptions correct so far?

Other things as I am thinking- 600rad/s is about 95.5Hz so each complete cycle from +6mm to -6mm should take .01s or so, so my answer should be less then that.

Last edited:
anyone?

I think I have it- if I then take

sin$$^{}-1$$(2/6)=600*T1?

sin$$^{}-1$$(-2/6)=600*T2?

then $$\Delta$$T is T1-T2?

does anyone have any input here?

pretty sure I've got it-

y1(x,t)=ym*sin(kx+600t1+$$\Phi$$)

2.00mm=6.00mm*sin(kx+600t1+$$\Phi$$)

sin$$^{}-1$$(1/3)=kx+600t1+$$\Phi$$

y2(x,t)=ym*sin(kx+600t2+$$\Phi$$)

-2.00mm=6.00mm*sin(kx+600t2+$$\Phi$$)

sin$$^{}-1$$(-1/3)=kx+600t2+$$\Phi$$

so...
[sin$$^{}-1$$(1/3)]-[sin$$^{}-1$$(-1/3)]=(kx+600t1+$$\Phi$$)-(kx+600t2+$$\Phi$$)

and...
[sin$$^{}-1$$(1/3)]-[sin$$^{}-1$$(-1/3)]=600t1-600t2

finally,

([sin$$^{}-1$$(1/3)]-[sin$$^{}-1$$(-1/3)])/600=t1-t2

do the math and $$\Delta$$t is .00113s

I think this is solved

no one ever responded to this guys problem, and now I'm actually trying to solve this as well and i tried doing the method he ended up using but i am not getting a correct answer. Although his method for the most part looks right and makes sense to me, the only thing I figure would be the problem is that x isn't a constant so they should cancel i don't think...but I'm not sure what else to do with so many unknown variables...any help?

## What is a "Wave on a string" problem?

A "Wave on a string" problem is a physics problem that involves studying the behavior of a wave as it travels along a string. The goal is to understand how different variables, such as tension, frequency, and amplitude, affect the properties of the wave.

## What is the equation for a wave on a string?

The equation for a wave on a string is given by y(x,t) = Asin(kx-ωt), where y is the displacement of the string, x is the position along the string, t is time, A is the amplitude of the wave, k is the wave number, and ω is the angular frequency.

## How does tension affect the speed of a wave on a string?

Tension has a direct effect on the speed of a wave on a string. As tension increases, the speed of the wave also increases. This is because higher tension results in a stiffer string, allowing the wave to travel faster.

## What is the relationship between frequency and wavelength in a wave on a string?

The relationship between frequency and wavelength in a wave on a string is inverse. As the frequency increases, the wavelength decreases, and vice versa. This relationship is described by the equation v = fλ, where v is the speed of the wave, f is the frequency, and λ is the wavelength.

## Can a wave on a string be reflected?

Yes, a wave on a string can be reflected when it encounters a boundary or obstacle. The angle of reflection is equal to the angle of incidence, and the wave's amplitude may change depending on the properties of the boundary or obstacle. This phenomenon is known as wave reflection.

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