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

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In summary, the conversation discusses the interference of two harmonic waves to produce a standing wave and the resulting distance between antinodes. It also introduces a new scenario with two harmonic waves and asks for the amplitude of the resultant wave. Lastly, it presents a question regarding the fundamental frequency of a vibrating string with four equal segments. The assumptions made include the distance between the first two antinodes being 4, the amplitude of the resultant wave being 6.4, and the fundamental frequency being 120 Hz.
  • #1
tanzerino
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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.


 
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  • #2
1st one is 4
 
  • #3
thanks for the help.
anyone can help me check the others?assumptions are my trials
 

1. What is the concept of superposition of two waves?

The superposition of two waves is a phenomenon in which two waves of the same type cross paths and combine to form a new wave. The resulting wave is the sum of the individual amplitudes of the two waves at each point in space and time.

2. How is the superposition of two waves calculated?

The superposition of two waves can be calculated by adding the individual amplitudes of the waves at each point. This can be represented mathematically as y = y1 + y2, where y is the resulting wave, y1 is the amplitude of the first wave, and y2 is the amplitude of the second wave.

3. What are the types of interference that can occur during superposition?

There are two types of interference that can occur during superposition: constructive interference and destructive interference. Constructive interference occurs when the two waves are in phase, meaning their crests and troughs align, resulting in a wave with a larger amplitude. Destructive interference occurs when the two waves are out of phase, resulting in a wave with a smaller amplitude or complete cancellation of the wave.

4. How does the frequency and wavelength of the two waves affect their superposition?

The frequency and wavelength of the two waves determine the resulting wave's frequency and wavelength during superposition. If the two waves have the same frequency and wavelength, the resulting wave will have the same frequency and wavelength. If the two waves have different frequencies and wavelengths, the resulting wave will have a frequency and wavelength that is a combination of the two.

5. What are some real-life applications of the superposition of two waves?

The superposition of two waves is used in many technological and scientific fields, such as acoustics, optics, and electronics. Some examples include noise-cancelling headphones, holograms, and radio antennas. Superposition is also used to study and understand natural phenomena, such as ocean waves and earthquake motions.

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