How Do Harmonic Waves Create Standing Waves and Affect String Vibrations?

  • Thread starter Thread starter tanzerino
  • Start date Start date
  • Tags Tags
    Waves
Click For Summary
SUMMARY

The discussion focuses on the interference of harmonic waves and their impact on string vibrations. Two harmonic waves, described by the equations y=3sin(0.25pi x)cos(10pi t) and y=4sin(3x-200t), create standing waves and result in specific amplitudes and frequencies. The distance between the first two antinodes is determined to be 4 meters, while the amplitude of the resultant wave is calculated to be 6.4. Additionally, the fundamental frequency of a string vibrating in four segments driven by a 480 Hz oscillator is identified as 120 Hz.

PREREQUISITES
  • Understanding of harmonic wave equations and their properties
  • Knowledge of standing wave formation and antinode calculation
  • Familiarity with wave amplitude and resultant wave calculations
  • Basic principles of string vibration and frequency determination
NEXT STEPS
  • Study the principles of wave interference and standing wave formation
  • Learn about the calculation of wave amplitudes using the superposition principle
  • Explore the relationship between frequency, tension, and length in vibrating strings
  • Investigate the effects of different oscillation frequencies on string vibrations
USEFUL FOR

Students and educators in physics, particularly those focusing on wave mechanics, as well as musicians and engineers interested in string instrument acoustics.

tanzerino
Messages
48
Reaction score
0
1. Two harmonic waves traveling in opposite directions interfere to produce a standing wave described by y=3sin(0.25pi x)cos(10pi t). What is the distance (in m) between the first two antinodes?
4
0.8
2
5
7



assumption 4?


Two harmonic waves are described by

y=4sin(3x-200t)
y=4sin(3x-200t-5)



What is the amplitude of the resultant wave?
4.3
4
8
6.4
5.7
assumption 6.4? as it is 2Acos(phase/2)...



Finally :s
A stretched string is observed to vibrate in four equal segments when driven by a 480 Hz oscillator. What is the fundamental frequency of vibration for this string?

Select the correct answer.
370Hz

120 Hz

245 Hz

619 Hz

494 Hz



assumption 120Hz as f proportional to n
Just tell me if anything is wrong please.thanks in advance.


 
Physics news on Phys.org
1st one is 4
 
thanks for the help.
anyone can help me check the others?assumptions are my trials
 

Similar threads

Which Frequency is NOT Possible for a Vibrating String?
  • · Replies 5 ·
Replies
5
Views
2K
Calculating Mass of a Vibrating String Using Known Quantities
  • · Replies 10 ·
Replies
10
Views
3K
Find two lowest frequencies standing wave
  • · Replies 5 ·
Replies
5
Views
6K
Standing waves on a fixed string
  • · Replies 3 ·
Replies
3
Views
5K
Standing Wave on String Question
  • · Replies 5 ·
Replies
5
Views
4K
How does increasing the tension of a string affect various properties?
  • · Replies 1 ·
Replies
1
Views
1K
How Does Water Leakage Affect the Frequency of a Vibrating Guitar String?
  • · Replies 1 ·
Replies
1
Views
2K
How Does Tension Affect the Frequency of Standing Waves?
  • · Replies 1 ·
Replies
1
Views
4K
How Do Tension and Length Affect Fundamental Vibrations on a String?
  • · Replies 1 ·
Replies
1
Views
2K
How Does Time Affect the Displacement of a Plucked Violin String?
  • · Replies 2 ·
Replies
2
Views
2K