Wave Theory Questions & Answers

Therefore, the displacement of the string at that point has to be zero, resulting in maximum amplitude.In summary, the conversation discusses the calculation of a wave equation for a string with one end tied to a wall, the conditions for a wave on a string with a loose end, and the resonance of a string when a short impulse is applied.
  • #1
pinsky
96
0
Hello there.

Can someone pleas shed lite on some of these questions.

How does one mathematically calculate (wave equation of a string that has one end tied on a unmoveable wall. The second wave is after reflecting from the wall) the first wave is known to us (u0 omega and k)

[tex]u_0 \; Sin(\omega t - kx)=- u_0' \; Sin(\omega t + kx + \phi)[/tex]

Conditions for a wave on a string which has a lose end. Why does that point has to always have a maximum amplitude when the string is oscillating?

When we apply a short impulse (force*time) on a string which is attached between two unmovable walls, does it always start to resonate? What determines the harmonic level of the resonation?


have a nice day
 
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  • #2
pinsky said:
Hello there.
Conditions for a wave on a string which has a lose end. Why does that point has to always have a maximum amplitude when the string is oscillating?
Because of your boundary condition the tangent to the string at the loose end have to be horizontal otherwise you would have a vertical component of force owed to the string tension
 
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What is Wave Theory?

Wave Theory is a branch of physics that describes the behavior and properties of waves. It explains how waves are created, how they move, and how they interact with different mediums. It is a fundamental concept in understanding many natural phenomena such as sound, light, and water waves.

What are the types of waves?

There are two main types of waves: mechanical waves and electromagnetic waves. Mechanical waves require a medium to travel through, such as sound waves or water waves. Electromagnetic waves do not require a medium and can travel through vacuum, such as light waves and radio waves.

What is the difference between frequency and wavelength?

Frequency and wavelength are two important properties of waves. Frequency is the number of complete cycles of a wave that occur in one second, measured in Hertz (Hz). Wavelength is the distance between two consecutive peaks or troughs of a wave, measured in meters (m). In simple terms, frequency is how often a wave occurs, while wavelength is the distance it travels.

What is the relationship between wave speed, frequency, and wavelength?

The speed of a wave is directly proportional to its frequency and wavelength. This means that as the frequency or wavelength increases, the speed of the wave also increases. This relationship is described by the equation: wave speed = frequency x wavelength.

How is wave interference explained in Wave Theory?

Wave interference is the phenomenon that occurs when two or more waves meet and interact with each other. In Wave Theory, interference is explained by the principle of superposition, which states that the displacement of a medium caused by two or more waves is the algebraic sum of the individual displacements. This can result in constructive interference (increased amplitude) or destructive interference (decreased amplitude) depending on the relative phase of the waves.

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