Need help with a few wave problems

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In summary, the problem is solved by finding the first two positive values of t that make y(0, t) = 0.303 m.
  • #1
feelau
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Hi, so here's the problem: A transverse wave on a string is described by the following equation. y(x, t) = (0.35 m) sin[(1.25 rad/m)x + (108.2 rad/s)t]
Consider the element of the string at x = 0. What is the time interval between the first two instants when this element has a position of y = 0.303 m? since the coefficient in front of the t variable is angular frequency which is equaled to 2pi/period, I thought I could just solve for the period and that is the time difference regardless of its position, but it's not correct so could anyone tell me how to go about solving this problem? I assume that my assumptions are flawed hehe... thank you for helping
 
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  • #2
Except for the points at which |y| is the amplitude, every y value is hit twice during each period of oscillation.
 
  • #3
so they actually mean half of the period?
 
  • #4
feelau said:
so they actually mean half of the period?
Not likely. Points that have the same displacement are not equally spaced. Look at a graph of the sine function.
 
  • #5
Then how should I go about solving this? The only idea I have is making this ito a triangle problem and finding out the angles and somehow relate it to distance and time
 
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  • #6
feelau said:
Then how should I go about solving this? The only idea I have is making this ito a triangle problem and finding out the angles and somehow relate it to distance and time
At x = 0 your equation

y(x, t) = (0.35 m) sin[(1.25 rad/m)x + (108.2 rad/s)t]

reduces to

y(0, t) = (0.35 m) sin[(108.2 rad/s)t]

You need to find the first two positive values of t that make y(0, t) = 0.303 m. Substitute this into the above equation and solve for t, then take the difference between the first two values of t that satisfy the condition.
 
  • #7
Would just graphing the function and finding where .303 intersects with the function ok?
 
  • #8
feelau said:
Would just graphing the function and finding where .303 intersects with the function ok?

You could do that but it would be more accurate to solve the problem analytically, which in this case is not too difficult. So, we have;

[tex]0.35\sin(108.2(t)) = 0.303[/tex]

What do you think the next step would be?
 
  • #9
WEll I'm not particularly good with trig so i don't know what the second solution would be... you just divide by .35, take arcsin and then divide by 108.2 but I only get one of the answer, I don't know how to get the other one :P
 
  • #10
feelau said:
WEll I'm not particularly good with trig so i don't know what the second solution would be... you just divide by .35, take arcsin and then divide by 108.2 but I only get one of the answer, I don't know how to get the other one :P

HINT: Sketch the graph of y=sin(x), where is the next solution going to be relative to your particular solution?
 
  • #11
But sketching it won't give us an exact solution though. I mean I guess I see where it's suppose to be but I don't know how to find it exactly using equations and such.
 
  • #12
feelau said:
But sketching it won't give us an exact solution though. I mean I guess I see where it's suppose to be but I don't know how to find it exactly using equations and such.
There are exact relations between the trig functions that can be seen from the symmetry of the curves. For example, the cos(x) is 1 at x = 0, and by symmetry cos(-x) = cos(x). Another example is sin(x) = 0 at x = 0 and by symmetry sin(-x) = -sin(x). You can make a similar symmetry observation for the first two angles that satisfy your equation. One very precise value can be obtained with the calculator, and another can by found using this one value and the symmetry of the graph.
 

Related to Need help with a few wave problems

What are wave problems and why are they important in science?

Wave problems refer to mathematical equations that describe the behavior of waves such as sound, light, and water. They are important in science because waves play a crucial role in many natural phenomena and technological applications.

What are the common types of wave problems?

The common types of wave problems include interference, diffraction, refraction, and standing waves. These problems involve the study of how waves interact with each other or with obstacles in their path.

How do I solve a wave problem?

To solve a wave problem, you need to understand the properties of waves and the mathematical equations that describe them. Start by identifying the type of wave problem and then use the appropriate mathematical formula to solve it.

What are the units of measurement for waves?

The units of measurement for waves depend on the type of wave being studied. For example, the units for sound waves are decibels, while the units for light waves are meters or nanometers. The units for measuring the speed of waves are meters per second.

What are some real-world applications of wave problems?

Wave problems have many real-world applications, such as in the fields of acoustics, optics, and seismology. They are also used in technologies like sonar, radar, and medical imaging. Understanding wave problems is crucial in designing and improving these technologies.

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