What is the value of ω for the following wave?

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In summary, there was confusion over the value of ω in a multi-dimensional harmonic wave equation. While the correct coefficient should have been ω=3*sqrt(5)*10^6, the answers provided a value of ω=3*sqrt(5)*10^14. It was also noted that the given expression for the wave may be a special case, with values for a and b adjusted to ensure orthogonality. However, no units were provided for the given answer.
  • #1
Eitan Levy
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Homework Statement
There is an electromagnetic wave with a magnetic component equal to:

Bsin(ax+by-3*sqrt(5)*10^6*t)(2x/3-y/3-2z/3) (The second set of parentheses represent the direction of the wave)

What is ω for this wave?
Relevant Equations
ω=kv
I am quite confused by this. I was sure that ω=3*sqrt(5)*10^6, because that is the coefficient of t, and generally u(x,y,z,t)=Asin(kx−ωt+ϕ) for a multi dimensional harmonic wave.

However in the answers it is said that ω=3*sqrt(5)*10^14. I can't see the reason for that, could anyone explain please?
 
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  • #2
What are the units in the answer that is given to you? What are the units in the answer that you think is correct? Do you have numbers and units for a and b?
 
  • #3
kuruman said:
What are the units in the answer that is given to you? What are the units in the answer that you think is correct? Do you have numbers and units for a and b?
No units were provided. The question is exactly what I wrote.
 
  • #4
Eitan Levy said:
Bsin(ax+by-3*sqrt(5)*10^6*t)(2x/3-y/3-2z/3) (The second set of parentheses represent the direction of the wave)
So using the LaTeX Guide at the bottom of the edit window, is this your expression?

$$ B sin(ax + by - 3\sqrt5 10^6 t) (\frac{2}{3}\hat x - \frac{1}{3} \hat y - \frac{2}{3} \hat z)$$

If so, it seems strange that the argument to the sin() function is dependent on x and y and t. But maybe I'm missing something... Maybe the medium that the wave is propagating though is non-isotropic?
 
  • #5
berkeman said:
So using the LaTeX Guide at the bottom of the edit window, is this your expression?

$$ B sin(ax + by - 3\sqrt5 10^6 t) (\frac{2}{3}\hat x - \frac{1}{3} \hat y - \frac{2}{3} \hat z)$$

If so, it seems strange that the argument to the sin() function is dependent on x and y and t. But maybe I'm missing something... Maybe the medium that the wave is propagating though is non-isotropic?

It is and there was a mistake in the answers.
 
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  • #6
berkeman said:
So using the LaTeX Guide at the bottom of the edit window, is this your expression?

$$ B sin(ax + by - 3\sqrt5 10^6 t) (\frac{2}{3}\hat x - \frac{1}{3} \hat y - \frac{2}{3} \hat z)$$

If so, it seems strange that the argument to the sin() function is dependent on x and y and t. But maybe I'm missing something... Maybe the medium that the wave is propagating though is non-isotropic?
The expression is probably a special case of $$\vec B(\vec r,t)=\vec B_0\sin(\vec k\cdot\vec r-\omega t)$$with ##k_x=a## and ##k_y=b##. Of course the values of ##a## and ##b## must be adjusted to ensure that the given direction of the field is orthogonal to the direction of propagation.
 
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Related to What is the value of ω for the following wave?

1. What is ω and how does it relate to waves?

ω, also known as angular frequency, is a measure of how quickly a wave oscillates. It is related to the frequency of a wave by the equation ω = 2πf, where f is the frequency in hertz. In simpler terms, ω tells us how many complete cycles a wave completes in one second.

2. How do you determine the value of ω for a given wave?

The value of ω for a wave depends on the type of wave and the properties of the medium it is traveling through. For example, in a simple harmonic wave, ω is equal to the square root of the ratio of the restoring force to the mass per unit length of the medium. In general, ω can be calculated using the wave equation specific to the type of wave being studied.

3. Does the value of ω change as the wave travels through different media?

Yes, the value of ω can change as a wave travels through different media. This is because the properties of the medium, such as density and elasticity, can affect the speed at which the wave travels. Since ω is related to the frequency and speed of a wave, it can also change as the wave moves through different media.

4. What is the significance of the value of ω in wave phenomena?

The value of ω is important in understanding various wave phenomena. It can help determine the amplitude, wavelength, and speed of a wave, as well as how it will interact with different media. In addition, ω is used in many mathematical equations that describe wave behavior, making it a crucial value in the study of waves.

5. Can the value of ω be negative?

No, the value of ω cannot be negative. Since it is related to the frequency of a wave, which is always a positive value, ω must also be positive. However, it can have a direction associated with it, such as clockwise or counterclockwise rotation, which can be represented by a positive or negative sign in mathematical equations.

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