Sound and Music - Mission SM7 Detailed Help

Consider the standing wave pattern for a guitar string as shown below. The speed of waves in the string is 462 m/s and the frequency associated with this pattern is 278 Hertz. Determine the wavelength (in centimeters) associated with this pattern and the length (in centimeters) of the string.  

(Note: Your numbers are selected at random and likely different from the numbers listed here.)


 
Length-Wavelength Relationship:
Each harmonic frequency is associated with a standing wave pattern. The 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 of vibrations is stated in units of meters per second. The length and wavelength must be determined in units of centimeters. At sometime during the solution of this problem, you will have to convert the unit meter to centimeters. Always be units-conscious.


 
Often times the development of an effective strategy is the most difficult part of a physics question. The strategy below should prove useful.
  1. Calculate the wavelength of the wave using the wave equation provided in the Formula Frenzy section.
  2. Convert the units on wavelength to centimeters. Enter the answer for wavelength.
  3. Analyze the provided standing wave pattern to determine the relationship between the wavelength of waves and the length of the string. See the Know the Law section.
  4. Use the length-wavelength relationship to calculate the length of the string in units of centimeters. Enter the answer for length.


 

The speed (v) of a wave is mathematically related to the wavelength (λ) and the frequency (f) of the wave. The relationship is expressed by the formula     

v = f • λ