Two pulses on the same string, where & when do they cancel?

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In summary, the task at hand is to find the instantaneous time at which two given wave equations cancel out and the position at which the pulses always cancel. The equations in question are y1 = 5/(kx − ωt)2 + 2 and y2 = −5/(kx + ωt − 6)2 + 2. The focus is on finding a method to deduce the values of t and x, rather than using equations directly. Attempts have been made, such as setting the two equations equal to each other, but no success has been achieved. Online resources have not been helpful in this particular type of question.
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Gavandeshaq
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Homework Statement


I've been given two wave equations:

y1 = 5/(kx − ωt)2 + 2
y2 = −5/(kx + ωt − 6)2 + 2

and I am to find first the instantaneous time at which they cancel, and then the position at which the pulses always cancel.

Homework Equations


This is the wave form equation, and it is already in that form. It seems more a matter of finding a method to deduce t and x, rather than by using equations.

The Attempt at a Solution


I've tried plugging in some values to see what exactly changes, and then used that information to decide how exactly to find the values, but to no avail. No web pages seem to have information relevant to this type of question.
 
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  • #2
An example of something I tried was setting the two equations equal to each other and then simplifying, but that didn't seem to work either.
 

1. What is the concept of "cancellation" in relation to two pulses on the same string?

The concept of "cancellation" refers to the phenomenon where two pulses traveling in opposite directions on the same string meet and produce a resultant pulse with zero amplitude. This means that the two pulses essentially cancel each other out, resulting in no disturbance on the string at that point.

2. What are the conditions for two pulses to cancel each other out on the same string?

For two pulses to cancel each other out, they must have equal amplitudes and be traveling in opposite directions on the same string. The timing of when they meet is also crucial, as they must meet at the exact same point on the string.

3. Can two pulses with different wavelengths cancel each other out on the same string?

No, two pulses with different wavelengths cannot cancel each other out on the same string. This is because the wavelength of a pulse determines its speed, and if they have different speeds, they will not meet at the same point on the string and will not cancel each other out.

4. What happens when two pulses do not have equal amplitudes but still meet on the same string?

If two pulses do not have equal amplitudes, they will not completely cancel each other out when they meet on the same string. Instead, the resultant pulse will have an amplitude that is equal to the difference between the two original pulses.

5. How does the medium in which the string is placed affect the cancellation of two pulses?

The medium in which the string is placed can affect the cancellation of two pulses in various ways. For example, if the medium is more dense, the pulses will travel at a slower speed and may not meet at the exact same point, resulting in incomplete cancellation. Additionally, the properties of the medium, such as its elasticity, can affect the amplitude and speed of the pulses, ultimately affecting their ability to cancel each other out.

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