Transverse wave equation period

In summary, the transverse wave equation period is the time it takes for one complete wave cycle to pass a fixed point in space. It is calculated by dividing the wavelength by the wave speed and is measured in seconds. The period and frequency of a transverse wave are inversely related, and can be changed by altering the wavelength or wave speed. This concept has various real-life applications, including in the study of electromagnetism, sound waves, and ocean waves, as well as in the design of musical instruments and electronic devices.
  • #1
james brug
34
0
A transverse wave on a rope is given by [tex]y(x, t)=
(0.750\; {\rm cm})\, \cos ( \, \pi [(0.400\;{\rm cm}^{ - 1})x+(250\; {\rm s}^{ - 1})t])[/tex]


Find the period.

This should be simple, but I keep getting the wrong answer in Mastering Physics. I can't find any explanation in my book, and it's really irritating me.
 
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  • #2
Rewrite the equation in a standard form.
y(x,t) = Acos[2*pi(x/lambda + t/T)]
Compare this with the given equation and find the period.
 
  • #3


I can understand your frustration with not being able to find the correct answer in Mastering Physics. It is important to carefully review the given equation and identify the variables involved. In this case, we have two variables, x and t, which represent distance and time respectively. The period of a wave is defined as the time it takes for one complete oscillation or cycle, and it can be calculated using the formula T=1/f, where T is the period and f is the frequency of the wave.

In the given equation, we can see that the frequency is represented by the coefficient in front of t, which is 250 s^-1. Therefore, to find the period, we simply need to take the reciprocal of this frequency, which would be 1/250 s or 0.004 s. This means that the wave completes one cycle every 0.004 seconds.

It is possible that the incorrect answer in Mastering Physics is due to a rounding error or a different method of calculation. I suggest double-checking your calculations and if the issue persists, seeking clarification from your instructor or a classmate. Remember to always carefully review the given equation and use the appropriate formulas to solve for the desired quantity.
 

1. What is the transverse wave equation period?

The transverse wave equation period is the time it takes for one complete wave cycle to pass a fixed point in space. It is represented by the symbol T and is measured in seconds.

2. How is the transverse wave equation period calculated?

The transverse wave equation period is calculated by dividing the wavelength (λ) by the wave speed (v). This can be expressed as T = λ/v.

3. How does the period of a transverse wave relate to its frequency?

The period and frequency of a transverse wave are inversely related. This means that as the period increases, the frequency decreases, and vice versa. The relationship can be expressed as T = 1/f, where f is the frequency in hertz (Hz).

4. Can the transverse wave equation period be changed?

Yes, the transverse wave equation period can be changed by altering the wavelength or the wave speed. For example, if the wavelength is increased, the period will also increase, resulting in a decrease in frequency.

5. What are some real-life applications of the transverse wave equation period?

The transverse wave equation period has many real-life applications, such as in the study of electromagnetism, sound waves, and ocean waves. It is also used in the design and analysis of musical instruments, as well as in the development of electronic devices such as radios and televisions.

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