# Power of a wave at a specific point

• lizzyb
In summary, the conversation discusses a wave pulse traveling along a string and its associated power. The given equation for the wave function includes a coefficient e^{-bx} and the book also has another equation for power. To find the power carried by the wave at a specific point, the value of A can be substituted into the equation using the given values.
lizzyb
Q: A wave pulse traveling along a string of linear mass density 0.0026 kg/m is described by the relationship $$y = A_0 e^{-bx}\sin(kx - \omega t)$$ where $$A_0 = 0.0097 m, b = 0.9 m^{-1}, k = .88 m^{-1} and \oemga = 56 s^{-1}$$. What is the power carried by this wave at the point $$x = 2.6 m$$?

My book has: $$\wp = \frac{1}{2} \mu \omega^2 A^2 v$$ which is the "power associated with the wave" but yet we're to show "the power carried by this wave at the point x = 2.6 m". Plus the equation given isn't a normal wave function - I guess - since it has the coefficient $$e^{-bx}$$.

The book also has $$\wp = \frac{E_\lambda}{\Delta t}$$ so if I had a $$\Delta x$$ I could so something similar as before, that is $$\wp_{\Delta x} = \frac{E_{\Delta x}}{\Delta t}$$ but this isn't the same thing?

How should I proceed? thanks.

Edit:
I guess I could take as A the whole $$A_0 e^{-bx}$$ and plug it into the equation (using the given values)?

Last edited:
lizzyb said:
Edit:
I guess I could take as A the whole $$A_0 e^{-bx}$$ and plug it into the equation (using the given values)?
That should do it. A is a time-decaying amplitude in this case.

fantastic! thanks! :-)

## 1. What is the power of a wave at a specific point?

The power of a wave at a specific point is the amount of energy that passes through that point per unit time. It is measured in watts (W) and can be thought of as the rate at which energy is transferred by the wave.

## 2. How is the power of a wave at a specific point calculated?

The power of a wave at a specific point can be calculated using the formula P = A²ρω²v, where P is power, A is amplitude, ρ is density of the medium, ω is angular frequency, and v is wave velocity. Alternatively, it can also be calculated using the formula P = E/T, where E is energy and T is time.

## 3. What factors affect the power of a wave at a specific point?

The power of a wave at a specific point is affected by a few factors, including the amplitude of the wave, the density and properties of the medium through which the wave is traveling, the frequency and wavelength of the wave, and any obstructions or barriers in the path of the wave.

## 4. How does the power of a wave at a specific point relate to its intensity?

The power of a wave at a specific point is directly related to its intensity, as both measures describe the strength or magnitude of the wave. Intensity is defined as the power of the wave per unit area, meaning that as the power increases, so does the intensity at that point.

## 5. Can the power of a wave at a specific point be negative?

No, the power of a wave at a specific point cannot be negative. This is because power is a measure of energy transfer, and energy transfer can only occur in a positive direction. If the power appears to be negative, it is likely due to a miscalculation or an error in measurement.

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