Ate of energy transfer by sinusoidal waves on a string q

In summary: Therefore, the energy per unit length is E/2pi r. This gives you the equation A²/2pi r = constant, or A ∝ 1/√r. In summary, the amplitude A at a distance r from the initial disturbance is proportional to 1/√r as shown by considering the energy carried by one outward-moving ripple.
  • #1
lizzyb
168
0
Q: A two-dimensional water wave spreads in circular wave fonts. Show that the aplitude A at a distance r from the initial disturbance is proportional to [tex]\frac{1}{\sqrt{r}}[/tex]. (Hint: Consider the energy carried by one outward moving ripple.)

Comments:
Let's consider the energy carried by one outward-moving ripple:
[tex]E_\lambda = \frac{1}{2} \mu \omega^2 A^2 \lambda[/tex]
and I suppose there is another wave directly across the origin for some particle. But how do I relate this to r?

thanks!
 
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  • #2
Consider the energy density of the ripple. That is the energy per unit length. The length of the wave being a circle is [tex]\pi r[/tex] and then consider the equation you have given above for energy as it contains the amplitude.
 
  • #3
lizzyb said:
Q: A two-dimensional water wave spreads in circular wave fonts. Show that the aplitude A at a distance r from the initial disturbance is proportional to [tex]\frac{1}{\sqrt{r}}[/tex]. (Hint: Consider the energy carried by one outward moving ripple.)

Comments:
Let's consider the energy carried by one outward-moving ripple:
[tex]E_\lambda = \frac{1}{2} \mu \omega^2 A^2 \lambda[/tex]
and I suppose there is another wave directly across the origin for some particle. But how do I relate this to r?

thanks!
All you really need to know to do this problem is that the energy is proportional to A². Since the wave is spreading out in a circle, the energy is being spread over the curcumference of the wave front.
 

Related to Ate of energy transfer by sinusoidal waves on a string q

What is energy transfer by sinusoidal waves on a string?

Energy transfer by sinusoidal waves on a string refers to the process of energy being transferred from one point to another through a string that is under tension. This transfer occurs through the propagation of sinusoidal waves, which are characterized by their amplitude, frequency, and wavelength.

How does energy transfer occur in this system?

In this system, energy transfer occurs through the vibration of the string. When the string is plucked or disturbed, it creates a disturbance that travels as a wave along the string. As the wave travels, it transfers energy from one point to another until it eventually dissipates.

What factors affect the rate of energy transfer in this system?

The rate of energy transfer in this system is affected by several factors, including the tension of the string, the amplitude and frequency of the waves, and the properties of the medium through which the wave is traveling. In general, higher tension and larger amplitudes result in faster energy transfer.

Can energy transfer by sinusoidal waves on a string be used for practical applications?

Yes, energy transfer by sinusoidal waves on a string has several practical applications. For example, it is used in musical instruments such as guitars and violins. It is also used in seismology to measure and study earthquakes, as well as in telecommunications for transmitting signals through fiber optic cables.

What are some real-world examples of energy transfer by sinusoidal waves on a string?

Some real-world examples of energy transfer by sinusoidal waves on a string include guitar strings vibrating to produce sound, seismic waves traveling through the Earth's crust during an earthquake, and fiber optic cables transmitting data through light waves. It can also be observed in everyday objects such as jumping ropes, springs, and slinkies.

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