Wave Motion - Mission WM8 Detailed Help

Jack and Jill create a standing wave pattern in a slinky by vibrating the slinky 51 times (i.e., 51 complete vibrational cycles) in 9.8 seconds. The pattern contains three loops between the ends of the slinky (the third harmonic). The slinky is stretched to a length of 2.6 meters. Determine the wavelength (in meters), frequency (in Hertz) and speed (in meters/second).
 
(Note: Your numbers are selected at random and likely different from the numbers listed here.)

 
 
Definition of Frequency:
The frequency of a wave refers to how often a repeating event takes place. It is the number of repetitions or cycles or vibrations occurring per unit of time.
 

Definition of Third Harmonic:
The third harmonic is the third lowest possible frequency with which a medium can vibrate and form a standing wave pattern. The third harmonic standing wave pattern is characterized by the presence of three loops (three antinodes) within the length of the medium.
 
This is a multi-step question that will be facilitated by the strategy outlined here:
  1. Determine the frequency at which the medium vibrates. Refer to the Dictionary section.
  2. Draw the standing wave pattern for this harmonic. Refer to the Dictionary section.
  3. Analyze the standing wave pattern which you have drawn. Write an equation in which you express the relationship between the length (L) of the rope and the number of one-half wavelengths. For example, L = 7•(1/2•λ). See Know the Law section.
  4. Substitute the value of L into your equation and solve for the wavelength (λ) of the rope.
  5. Use the wave equation (see Formula Frenzy section) to determine the speed of the waves.



 
Analysis of a Standing Wave Pattern:
A standing wave pattern shows a unique relationship between the wavelength of the waves that create the pattern and a length measured along the medium between two points on the pattern. Every nodal position on the pattern is separated from the next adjacent nodal position by one-half of a wavelength. Similarly, every antinodal position on the pattern is separated from the next adjacent antinodal position by one-half of a wavelength.


 
The speed (v) of a wave can be calculated from knowledge of the wavelength ( λ) and the frequency (f) of the wave. The formula is       

v = f • λ