Standing Waves Tension and wavelength

In summary, the conversation revolved around the derivation of the wave equation for a string under tension using the laws of motion. The asker was unsure of where the square root was coming from in the equations and received helpful resources to understand the concept further. Eventually, they were able to figure it out through additional research.
  • #1
xtrubambinoxpr
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Homework Statement



Please see the picture.

Homework Equations



How do they get this derivation?

The Attempt at a Solution



I know that lambda = 2L/n and f = nV/2L so I can somewhat rearrange it myself, but I do not know where the square root is coming from.
 

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  • #3

Related to Standing Waves Tension and wavelength

What are standing waves?

Standing waves are a type of wave that occurs when two waves with the same frequency and amplitude travel in opposite directions and interfere with each other. This creates a pattern of nodes and antinodes where the amplitude of the wave remains constant.

How does tension affect standing waves?

Tension in a medium, such as a string or rope, affects the speed at which a wave travels. The higher the tension, the faster the wave will travel. This means that higher tension will result in a shorter wavelength and a higher frequency for standing waves.

What is the relationship between wavelength and frequency in standing waves?

The wavelength of a standing wave is determined by the length of the medium and the number of nodes and antinodes present. The frequency of the standing wave is directly proportional to the wavelength, meaning that as the wavelength increases, the frequency also increases.

How can standing waves be created?

Standing waves can be created by a variety of methods, such as plucking a string or using a tuning fork. The key is to have two waves with the same frequency and amplitude traveling in opposite directions and interfering with each other.

What is the significance of standing waves in science and technology?

Standing waves have many practical applications, including in musical instruments, where they produce distinct tones and harmonics. They are also used in various types of engineering, such as in antennas and resonators. Understanding standing waves is crucial in the fields of acoustics and optics as well.

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