Wave- displacement for a point

In summary: Can you use the other equation, 0.01=0.02sin(2.63t1), to find t1?In summary, the conversation discusses finding the shortest time for the displacement of a wave on a string to change from 0.01m to -0.02m. The solution involves setting x=0 and solving for t1 and t2 using the equations 0.01=0.02sin(2.63t1) and 0.02sin(2.63t2)=-0.02. The solution given in the conversation is incorrect, and the student is asked to find alternative values for t1 and t2 that satisfy the equations.
  • #1
scrubber
20
0

Homework Statement



A wave on a string has a wave function with the form of:
y(x,t)=0.02sin(6.35x+2.63t)

Find the shortest time for the displacement of the string at any point on the chain changes from 0.01m to -0.02m.

The Attempt at a Solution



The answer said we can set x=0.
And 0.01=0.02sin(2.63t1), 3*3.14/2=2.63t2, where t1 is initial time and t2 is final time.
then t1=0.2s and t2=1.6s, so t2-t1=1.4s

But I don't understand where 3*3.14/2=2.63t2 comes from.
And when I tried to follow the answer and calculate, the calculated answers don't seem to be correct...

So how should I solve it?
Thank you very much.
 
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  • #2
scrubber said:
But I don't understand where 3*3.14/2=2.63t2 comes from.
And when I tried to follow the answer and calculate, the calculated answers don't seem to be correct...

So how should I solve it?
Thank you very much.

At t2, the displacement is -0.02 at x=0. 0.02 sin(2.63 t2)=-0.02--> sin(2.63 t2)=-1. What is the angle if its sine is -1?

ehild
 
  • #3
ehild said:
At t2, the displacement is -0.02 at x=0. 0.02 sin(2.63 t2)=-0.02--> sin(2.63 t2)=-1. What is the angle if its sine is -1?

ehild

270 degree, and why does the angle matter please?
 
  • #4
well, you have the equation 0.02 sin(2.63 t2) = -0.02 And you want to find t2, right? So what is the usual way to find t2 from here?

Also, remember there are many possible values for the angle, so there are many possible values for t1 and t2. But they want you to find values for t1 and t2 such that t2-t1 is as close to zero as possible.
 
  • #5
BruceW said:
well, you have the equation 0.02 sin(2.63 t2) = -0.02 And you want to find t2, right? So what is the usual way to find t2 from here?

Also, remember there are many possible values for the angle, so there are many possible values for t1 and t2. But they want you to find values for t1 and t2 such that t2-t1 is as close to zero as possible.

I got that now!
That means 2.63 t2 = 3/4∏, right?
But still, the calculated t2 is 1.79, which is not 1.6 from the solution. Anything wrong?
 
  • #6
There are many possible correct pairs of t1 & t2. In the solution, they use the pair 0.2s & 1.6s
You have found 1.79s as a solution for t2. So you need to find a value for t1 which matches this value of t2.
OR, you can just try to find t2=1.6s instead. So, your equation was sin(2.63 t2) = -1 Can you find some other angles that will work here?
 
  • #7
hey, wait a minute.. I think their pair 0.2 & 1.6 does not work. Yeah, I'm pretty sure the solution is wrong. Anyway, keep going with your solution. You have got a value for t2. So now you need to find a value for t1.
 

1. What is wave displacement for a point?

Wave displacement for a point is the measure of the distance a point on a wave has moved from its equilibrium position. It is typically measured in units of length, such as meters or centimeters.

2. How is wave displacement calculated?

Wave displacement is calculated by subtracting the equilibrium position from the current position of the point on the wave. This can be done for any point on the wave at any given time.

3. What is the relationship between wave displacement and amplitude?

The amplitude of a wave is directly related to its displacement. The greater the displacement, the higher the amplitude of the wave will be. However, displacement only measures the distance from equilibrium, while amplitude also takes into account the height of the wave.

4. How does wave displacement change over time?

Wave displacement changes over time as the wave moves through space. The point on the wave will continue to move back and forth, changing its displacement from the equilibrium position as the wave passes through it. The rate of change of displacement over time is known as the velocity of the wave.

5. What factors can affect wave displacement?

The factors that can affect wave displacement include the amplitude of the wave, the frequency of the wave, and the medium through which the wave is traveling. Changes in any of these factors can alter the displacement of a point on the wave.

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