Transverse displacement, tricky MC

In summary, the transverse displacement of a stretched string from equilibrium as a function of time and position can be represented by the equation y=0.13cos(3x+27t), where x and y are in meters and t is in seconds. Using this equation, we can determine various properties of the wave. The period can be found using the formula T=2pi/omega, giving a value of 0.23s. This indicates that the period is greater than 0.1s. We can also determine that the wave has a speed of 8m/s and a wavelength of 1m. Furthermore, the wave moves in the positive x direction.
  • #1
K3nt70
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Homework Statement



The transverse displacement of a streched string from equilibrium as a function of time and position is given by:
y=0.13cos(3x+27t). x and y are in m; t is in s.
(Select T-True, F-False, G-Greater than, L-Less than, E-Equal to, If the first is T and the rest F, enter
TFFF).

A) The speed of the wave is ... 8 m/s
B) The wavelength is ... 1 m
C) The wave moves in the positive x direction
D) The period is ... 0.1 s

Homework Equations



The only one i was able to solve for was D, using

[tex]\omega[/tex] = [tex]\frac{2\pi}{T}[/tex]

The Attempt at a Solution



Solving for T: T= 2pi/27 gives T= 0.23 s. This designates D as G (greater than).
I can't really figure out how we get the others from T... My main problem is Finding velocity. If i find velocity, i can find the rest. My secondary problem is finding out the direction of the wave.

p.s. even my tutor couldn't get this one.
 
Last edited:
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  • #3
Got it worked out, thanks. My problem was not recognizing what k was in this situation (angular wave number).
 

1. What is transverse displacement?

Transverse displacement refers to the movement of an object perpendicular to its original position. In other words, it is the distance an object moves side to side from its equilibrium point.

2. How is transverse displacement measured?

Transverse displacement is typically measured in units of length, such as meters or centimeters. It can be measured using tools such as rulers, calipers, or displacement sensors.

3. What is the difference between transverse displacement and longitudinal displacement?

Transverse displacement refers to side-to-side movement, while longitudinal displacement refers to movement along the length of an object. Think of transverse displacement as a swinging motion and longitudinal displacement as a back and forth motion.

4. How does transverse displacement affect wave behavior?

Transverse displacement is a key factor in wave behavior, particularly in transverse waves. It determines the amplitude of the wave, which is the maximum displacement from the equilibrium point. It also affects the wavelength, which is the distance between two consecutive points of equal displacement.

5. Can transverse displacement be negative?

Yes, transverse displacement can be negative. This means that the object has moved in the opposite direction from its equilibrium point. This can occur in both transverse and longitudinal waves, depending on the direction of the wave's motion.

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