How Do Sinusoidal Waves Interfere to Form a Resultant Wave?

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In summary, "Identical Except for Phase" refers to systems that have the same physical properties but differ in timing or position. Examples include pendulums and waves. Phase difference can affect the behavior of these systems, but under certain conditions, they can become completely synchronized. This concept is used in scientific research to understand the impact of small differences in timing or position on complex systems.
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matt62010
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Two sinusoidal waves, identical except for phase, travel in the same direction along a string and interfere to produce a resultant wave given by y' (x, t) = (1.5 mm) sin(29x - 4.0t + 0.980 rad), with x in meters and t in seconds.
(a) What is the wavelength, λ, of the two waves?
m
(b) What is the phase difference between them?
rad
(c) What is their amplitude Y?
mm

sorry, but i have no idea how to do this problem. any help is greatly appreciated!
 
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  • #2
Doesn't your textbook discuss traveling waves, and provide equations that would be relevant?
 
  • #3


No problem! Let's break down the problem step by step to better understand it.

First, we have two sinusoidal waves that are traveling in the same direction along a string. This means that they have the same amplitude, frequency, and wavelength. The only difference between them is their phase.

(a) To find the wavelength, we can use the formula: λ = v/f, where λ is the wavelength, v is the velocity of the wave, and f is the frequency. In this case, we are given the frequency (29 Hz) and the velocity (unknown), so we need to rearrange the formula to solve for the wavelength.

Using the given equation, we can see that the coefficient of x is equal to 29, which is the frequency. This means that the velocity of the wave must be 29 m/s. Now, we can plug in the values into the formula to find the wavelength:

λ = (29 m/s) / (29 Hz) = 1 m

Therefore, the wavelength of the two waves is 1 meter.

(b) The phase difference between the two waves can be found by looking at the coefficient of t in the given equation. In this case, it is -4.0, which means that the phase difference is 4 radians. This also tells us that the two waves are out of phase by 4 radians.

(c) Finally, to find the amplitude of the waves, we can simply look at the coefficient of the sine term, which is 1.5 mm. This means that the amplitude of the waves is 1.5 mm.

So, to summarize:

(a) Wavelength = 1 meter
(b) Phase difference = 4 radians
(c) Amplitude = 1.5 mm

I hope this helps! Let me know if you have any other questions.
 

FAQ: How Do Sinusoidal Waves Interfere to Form a Resultant Wave?

1. What is meant by "Identical Except for Phase" in the context of science?

In science, "Identical Except for Phase" refers to two or more objects or systems that have the same physical properties and characteristics, but differ in the timing or position of their cycles or oscillations.

2. What are some examples of systems that can be considered "Identical Except for Phase"?

Some examples of systems that can be considered "Identical Except for Phase" include pendulums, sound waves, and electromagnetic waves.

3. How does phase difference affect the behavior of "Identical Except for Phase" systems?

The phase difference between two "Identical Except for Phase" systems can cause them to exhibit different behaviors. For example, two pendulums with the same length and weight but different starting positions will have different oscillation patterns due to their phase difference.

4. Can "Identical Except for Phase" systems ever become completely synchronized?

Yes, under certain conditions, "Identical Except for Phase" systems can become completely synchronized. This phenomenon is known as phase locking and occurs when the phase difference between the systems is reduced to zero.

5. How is the concept of "Identical Except for Phase" used in scientific research?

The concept of "Identical Except for Phase" is used in various fields of science, such as physics and biology, to study the behavior and interactions of systems with similar physical properties but different phase differences. It helps scientists understand how small changes in timing or position can have a significant impact on the behavior of complex systems.

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