Ξ cm = 4.9 sin (1.06 x - 0.77 t) - Determine Travelling Speed of Wave

In summary, the equation of a wave along the x-axis is given as ξ cm = 4.9 sin (1.06 x - 0.77 t), with units of 1/cm for К and 1/s for ω. The traveling speed of the wave can be determined by using the formula V = ω/k, where ω is the frequency and k is the wavelength. Plugging in the values, we get V = 0.77/1.06 = 0.726, which is the wrong answer. Another way to calculate the speed is by using the formula V = f*λ, where f is the frequency and λ is the wavelength. Using the values 2π/1
  • #1
05holtel
52
0

Homework Statement



The equation of a wave along the x-axis is given as: ξ cm = 4.9 sin (1.06 x - 0.77 t)
in which ξ is the displacement. Units on the right hand side are 1/cm for К and 1/s for ω.
Determine the the traveling speed of the wave.
Express the result in the unit m/s and to three significant figures. If you must use scientific notation, please enter as follows: e.g. 0.000123 = 1.23E-4. Only answer in numerical values, no units. For negative numbers, leave no space between the negative sign and the number: e.g. right: -1.00, wrong: - 1.00.


Homework Equations



I would think V= w/k

The Attempt at a Solution



V = 0.77/1.06
= 0.726

This is the wrong answer
 
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  • #2
lambda = 2*pi/1.06
frequency f = 2*pi/077
v = f*lambda.
Try this one.
 
  • #3
(2*pi/1.06)(2*pi/0.77)
v = 48.3

It says it is wrong. Are the units m/s?
 
  • #4
Your initial method is correct. Try writing in the units to see what units your answer is in and then convert it if necessary.
 

Related to Ξ cm = 4.9 sin (1.06 x - 0.77 t) - Determine Travelling Speed of Wave

1. How do you determine the travelling speed of a wave using the formula Ξ cm = 4.9 sin (1.06 x - 0.77 t)?

The travelling speed of a wave can be determined by looking at the coefficient of t in the formula Ξ cm = 4.9 sin (1.06 x - 0.77 t). In this case, the coefficient is -0.77. This value represents the speed of the wave in units of distance per unit time.

2. What do the variables x and t represent in the formula Ξ cm = 4.9 sin (1.06 x - 0.77 t)?

The variable x represents the position of a point on the wave, while t represents the time at which the position is measured. Together, they create a wave function that describes the motion of the wave over time.

3. What is the significance of the coefficient 1.06 in the formula Ξ cm = 4.9 sin (1.06 x - 0.77 t)?

The coefficient 1.06 represents the wave number, which is a measure of how many complete waves occur in a certain distance. It is related to the wavelength of the wave, with a larger wave number indicating a shorter wavelength.

4. How does the amplitude of the wave affect its travelling speed?

The amplitude of a wave does not directly affect its travelling speed. However, a wave with a larger amplitude will have a greater energy and therefore may travel faster or farther than a wave with a smaller amplitude.

5. Can the formula Ξ cm = 4.9 sin (1.06 x - 0.77 t) be used for all types of waves?

No, this formula specifically describes the motion of a sinusoidal wave. Other types of waves, such as transverse or longitudinal waves, have different equations that describe their motion.

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