Energy in each cycle of transverse wave?

In summary, energy is transferred in a transverse wave through the vibration of particles in a medium perpendicular to the direction of the wave's motion. The amplitude of a transverse wave directly affects its energy, with larger amplitudes carrying more energy. The wavelength and energy of a transverse wave are inversely proportional, while the frequency and energy are directly proportional. As a transverse wave travels through different mediums, its energy remains constant but the speed, wavelength, and frequency may change due to the principle of conservation of energy.
  • #1
Sho Kano
372
3

Homework Statement


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Homework Equations

The Attempt at a Solution


a. ##{ P }_{ avg }=\frac { 1 }{ 2 } \mu v{ \omega }^{ 2 }{ A }^{ 2 }=\frac { 1 }{ 2 } 0.075\frac { 10 }{ 3 } { 0.35 }^{ 2 }{ (10\pi ) }^{ 2 }=15.1W##
b. Not sure how to calculate that... I'm guessing it'd be some integral over 1 period for the kinetic energy involved in the up down movement of the string plus some integral for the potential energy involved with the string's tension over 1 wavelength. How do I construct these integrals?
 
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  • #2
Never mind! ##\omega =10\pi =\frac { 2\pi }{ T } \\ T=\frac { 1 }{ 5 } s\\ PT=\frac { J }{ s } s=J=15\frac { 1 }{ 5 } =3J##
 
  • #3
I know I can do this using an integral. But how?
 

FAQ: Energy in each cycle of transverse wave?

1. How is energy transferred in a transverse wave?

In a transverse wave, energy is transferred through the vibration of particles in a medium perpendicular to the direction of the wave's motion. This means that as the wave moves up and down, the particles also move up and down, transferring energy from one particle to the next.

2. How does the amplitude of a transverse wave affect its energy?

The amplitude of a transverse wave, which is the maximum displacement of particles from their rest position, directly affects the energy of the wave. The greater the amplitude, the more energy the wave carries. This is because larger amplitudes require more energy to move the particles further from their resting position.

3. What is the relationship between wavelength and energy in a transverse wave?

The wavelength of a transverse wave, which is the distance between two consecutive peaks or troughs, is inversely proportional to the energy of the wave. This means that as the wavelength increases, the energy of the wave decreases and vice versa.

4. How does frequency affect the energy of a transverse wave?

The frequency of a transverse wave, which is the number of complete wave cycles per second, is directly proportional to the energy of the wave. This means that as the frequency increases, the energy of the wave also increases.

5. What happens to the energy of a transverse wave as it travels through different mediums?

The energy of a transverse wave remains constant as it travels through different mediums. However, the speed of the wave may change, which can affect the wavelength and frequency of the wave. This is known as the principle of conservation of energy.

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