Standing Waves: Finding the number of antinodes

In summary, in a string with a fixed frequency vibrator at one end, under tension T1, a standing wave with 4 antinodes is formed. When tension is slowly increased, the standing wave disappears until tension T2 is reached, with no resonances occurring between the two tensions. The new standing wave would have 5 antinodes, as the number of antinodes increases by one as the tension increases from one resonant tension to the next.
  • #1
Turion
145
2

Homework Statement



A string with a fixed frequency vibrator at one end forms a standing wave with 4 antinodes when under tension T1. When the tension is slowly increased, the standing wave disappears until tension T2 is reached with no resonances occurring between the two tensions. How many antinodes are there in this new standing wave?

Homework Equations


The Attempt at a Solution



There would be 8 antinodes, right? Because as you jump up to the next frequency, the number of antinodes doubles.

Actually, no, it would be 5 antinodes, right?
 
Last edited:
Physics news on Phys.org
  • #2
I believe it would be 5 antinodes. Going from a given resonant tension to the next increases the number of antinodes by one.
 

1. What are standing waves?

Standing waves are a type of wave that forms when two identical waves with the same frequency and amplitude travel in opposite directions and interfere with each other. This results in points of maximum and minimum amplitude, known as nodes and antinodes, respectively.

2. How do you find the number of antinodes in a standing wave?

The number of antinodes in a standing wave is equal to the number of half wavelengths present in the wave. This can be calculated by dividing the length of the wave by the wavelength, or by counting the number of peaks and troughs in the wave pattern.

3. What is the relationship between wavelength and the number of antinodes?

The wavelength of a standing wave is directly proportional to the number of antinodes. As the wavelength increases, the number of antinodes also increases, and vice versa.

4. How does the amplitude affect the number of antinodes?

The amplitude of a standing wave does not affect the number of antinodes. The number of antinodes is solely determined by the frequency and wavelength of the wave.

5. What applications do standing waves have in science?

Standing waves have various applications in science, including in musical instruments, where they are responsible for producing specific notes and tones. They are also used in certain imaging techniques, such as ultrasound, and can be used to measure properties of materials, such as elasticity and density.

Similar threads

Describing the Motion of a String at the Antinodes
    • Introductory Physics Homework Help
Replies
12
Views
2K
Calculating Mass of a Vibrating String Using Known Quantities
    • Introductory Physics Homework Help
Replies
10
Views
2K
Find two lowest frequencies standing wave
    • Introductory Physics Homework Help
Replies
5
Views
5K
Effect of temperature on vibrational frequency of a violin string
    • Introductory Physics Homework Help
Replies
5
Views
835
Resonance box with tuning fork, standing wave
    • Introductory Physics Homework Help
Replies
4
Views
2K
Finding Nodes in a Standing Wave at 800 Hz
    • Introductory Physics Homework Help
Replies
4
Views
4K
Find Energy of Antinode & Node in Standing Wave of Time Period T
    • Introductory Physics Homework Help
Replies
16
Views
3K
Standing waves on string with increasing tension
    • Introductory Physics Homework Help
Replies
3
Views
5K
Finding the Location of the 2nd Antinode in a Standing Wave at 4.10 Meters
    • Introductory Physics Homework Help
Replies
4
Views
2K
Standing Waves: Synchronization between a Tube & a Stick
    • Introductory Physics Homework Help
Replies
6
Views
2K

Hot Threads

Recent Insights

Back
Top