Zwiebach 9.3e: Relating τ to X0 & Angular Frequency

  • Thread starter ehrenfest
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In summary, the period of a wave (τ) is related to its amplitude (X0) and angular frequency (ω) through the equation τ = 2πX0/ω. To calculate the period, you need to know the amplitude and angular frequency. The unit of measurement for period is typically seconds (s). Changing the amplitude or angular frequency will result in a longer or shorter period, respectively, as they are directly and inversely proportional to the period.
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ehrenfest
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Homework Statement


I can relate tau and X0 by:

[tex] \tau = \frac{X^0}{2 \sqrt{2} \alpha' p^+ } [/tex]

Why does that mean the angular frequency is

[tex] \frac{1}{2 \sqrt{2} \alpha' p^+ } [/tex]

?

Homework Equations





The Attempt at a Solution

 
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  • #2
ehrenfest said:
[tex] \tau = \frac{X^0}{2 \sqrt{2} \alpha' p^+ } [/tex]
Take this and plug it into the equations for [itex]X^{(2)}[/itex] and [itex]X^{(3)}[/itex].
 

1. What is the relationship between τ, X0, and angular frequency?

The relationship between τ (period), X0 (amplitude), and angular frequency is given by the equation τ = 2πX0/ω, where ω represents the angular frequency.

2. How do I calculate the period of a wave using its amplitude and angular frequency?

You can calculate the period of a wave by using the equation τ = 2πX0/ω, where X0 is the amplitude and ω is the angular frequency.

3. Can the period of a wave be determined without knowing its amplitude?

No, in order to calculate the period of a wave using the equation τ = 2πX0/ω, you need to know the amplitude (X0) and the angular frequency (ω).

4. What is the unit of measurement for the period of a wave?

The unit of measurement for the period of a wave is typically seconds (s) since it represents the time it takes for one complete cycle of the wave.

5. How does changing the amplitude or angular frequency affect the period of a wave?

Increasing the amplitude of a wave will result in a longer period, while increasing the angular frequency will result in a shorter period. This is because the period is directly proportional to the amplitude and inversely proportional to the angular frequency.

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