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

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Two harmonic waves traveling in opposite directions can create a standing wave, exemplified by the equation y=3sin(0.25pi x)cos(10pi t), with the distance between the first two antinodes calculated as 4 meters. The amplitude of the resultant wave from two given harmonic waves is debated, with a proposed value of 6.4 based on the formula 2Acos(phase/2). Additionally, a stretched string vibrating in four segments driven by a 480 Hz oscillator leads to the conclusion that the fundamental frequency is 120 Hz, as frequency is proportional to the number of segments. Participants in the discussion are seeking confirmation of their calculations and assumptions. Overall, the thread focuses on the principles of wave interference and string vibrations.
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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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1st one is 4
 
thanks for the help.
anyone can help me check the others?assumptions are my trials
 
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