Amplitude relation with periodic time

In summary, the question asks which sound wave, with a frequency of either 100 Hz or 500 Hz, will have its crests farther apart. The student attempted to find the periodic time for each wave and found that the second wave had a larger wavelength, making it slower than the first wave. However, they were unable to determine the amplitude using the given information. The question does not mention amplitude, so it is unclear if there is a relation between periodic time, wavelength, and amplitude. The student is advised to look for an equation in their textbook that relates wave velocity, frequency, and wavelength.
  • #1
SakuRERE
68
5

Homework Statement


Ql: Which sound wave will have its crests farther apart from each other - a wave with frequency 100 Hz or a wave with frequency 500 Hz?

Homework Equations


Frequency= 1/ periodic time

The Attempt at a Solution


I did it like that:
I just found the periodic time for each wave, substituting in the previous relation. and I ended up with :
first wave (500Hz) => 0.002 s
second wave (100 Hz) => 0.01 s

which means that the second has larger wavelength making it ~slower (if we can say), and the first one with a larger wavelength.
however, I still can't reach the crest (amplitude) using the given information!

is there any relation between the periodic time and the amplitude?
or the wavelength and the amplitude?

thanks in advance
 
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  • #2
I read the question's use of "farther apart" as relating to distance. You would then need an equation that involves some sort of length.
 
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  • #3
SakuRERE said:
is there any relation between the periodic time and the amplitude?
or the wavelength and the amplitude?
You ask about amplitude there in what I quoted and in your thread title, but it is not in the problem statement as far as I can see. Is there more to the problem statement?
 
  • #4
Look in your textbook for the equation that relates a waves velocity, frequency and wavelength.
 

1. What is the relationship between amplitude and periodic time?

The amplitude of a periodic motion is the maximum displacement of the object from its equilibrium position. The periodic time, also known as the period, is the time it takes for the object to complete one full cycle of motion. The relationship between amplitude and periodic time is that as the amplitude increases, the periodic time also increases.

2. How does changing the amplitude affect the periodic time?

Changing the amplitude of a periodic motion will affect the periodic time by increasing or decreasing it. This is because the larger the amplitude, the longer it takes for the object to complete one full cycle of motion. On the other hand, a smaller amplitude will result in a shorter periodic time.

3. Is there a mathematical formula for the relationship between amplitude and periodic time?

Yes, the mathematical formula for the relationship between amplitude and periodic time is T = 2π√(m/k), where T is the periodic time, m is the mass of the object, and k is the spring constant. This formula is known as the period equation and shows that the periodic time is inversely proportional to the square root of the spring constant.

4. How does the amplitude affect the energy of a periodic motion?

The amplitude of a periodic motion does not directly affect the energy of the system. The energy of a periodic motion is determined by the mass, velocity, and position of the object. However, a larger amplitude may result in a larger displacement and therefore a larger potential energy.

5. Can the relationship between amplitude and periodic time be applied to all types of periodic motion?

Yes, the relationship between amplitude and periodic time is a fundamental principle that applies to all types of periodic motion, including simple harmonic motion, pendulum motion, and circular motion. This relationship is based on the properties of the system, such as mass and spring constant, and therefore can be applied universally.

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