Standing Waves on a String, Fundamental Frequency, Harmonics, Overtones, Nodes, Antinodes, Physics
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- Опубліковано 26 лис 2016
- This Physics video tutorial explains the concept of standing waves on a string. It shows you how to calculate the fundamental frequency and any additional harmonics or overtones. In addition, it shows you how to identify and count the number of nodes and antinodes on a standing wave given the number of loops. This video contains plenty of examples and physics practice problems.
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Here is a list of topics:
1. Standing Waves on a String
2. Number of Loops - Length of String vs Wavelength
3. Trough vs Crest
4. Tension Force, Wave Speed, and Linear Density of String / Wire
5. Frequency, Wavelength, and Wave Speed Calculations
6. Fundamental Frequency, Harmonics and Overtone Problems
7. Nodes and Antinodes - Physics
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13:41 A standing wave has 5 loops. How many nodes and antinodes are present?
14:46 The fundamental frequency of a certain standing wave is 175 Hz. Calculate the first 4 harmonics.
16:12 The 7th Harmonic of a standing wave is 280 Hz. What is the frequency of the 4th and 9th Harmonic?
17:35 A 2 meter string produces a standing wave with 3 loops.
a) What is the standing wavelength?
18:56 b) What is the frequency if the speed of the wave is 45 m/s?
20:00 c) What is the wavelength and speed of the first harmonic?
22:37 The wavelength of a standing wave with one loop is 12 meters. Find the wavelength of the first five harmonics.
23:38 The wavelength of 5th harmonic is 1.8 meters. Calculate the wavelength of the 9th harmonic.
24:56 A standing wave with a speed of 30 m/s and five loops has a frequency of 250 Hz.
a) What is the length of the string in centimeters
27:19 b) If the string has a mass of 40 g, what tension force is required to produce such a wave?
29:56 A tension force of 300N was applied to a 0.75kg string that is 5 meters long. A standing wave with 5 loops was produced.
Calculate the:
a) speed
31:44 b) wavelength
32:58 c) frequency
d) fundamental frequency
and the first three overtones
36:38 The frequency of the 4th harmonic is 300 Hz and the wavelength of the 2nd harmonic is 2.3 meters. What is the speed of the wave?
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4:45 Note that: L=nλn/2 i.e. λn=2l/n(1). v=λf i.e. λ=v/f(2). From equations 1 and 2, v/f=2l/n i.e. f=nv/2l. When n=1, the frequency is said to be fundamental.
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You could just multiply 2.3 x 2 then divide by 4 to get both with the same n value then multiply the 1.15 by 300. I found that to be easier.
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Wonderful indeed. But, please I would like to ask, is it a must to use it the 7th harmonic, to find the first?.
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I have the following problem could you please help me to solve it? 3. A spring and mass system with a mass of 2.5 kg is observed to have a frequency of 5.5 Hz. What is the stiffness constant of the spring?
Hey I wrote 4/3 as a whole decimal number so I got 67.5 do you think I would still get it right in the exam?
Can someone explain why there are different types of standing waves created whenever you pluck a string?
How about a series on transmission line theory?
Question; Nods represent the displacement to an anti nod... In space as a energy is transimited or Non tansit. Can we infer that the Nodes is the missing dark matter & energy we have been seeking...?
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25:33 If I use fn = (vn)/(2L), I've got different answer. Could anyone please tell me why?
I got a different answer too!
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Hi, @23:08 the questions stated that standing wave only has one loop. How can you have multiples wavelength with just one loop? I thought one loop= 1 wavelength.
20:00 How did you get f3?
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What does 'n' and 'L' represent? I have been following velocity (wave speed m/s), frequency (Hz) and lambda (wavelength), so I'm a bit confused.
n is the number of loops or harmonics and L is the length of the string
can someone tell me in 21:05 lambda(n) = lambda(1)/n but in the next line its lambda(1) = nlambda(n)? parenthesis represent subscripts
28:16 Why multiply the right side only with L? Why not multiply the before = and after = because that would make sense to me. I’m confused.
Edit: and why multiply by L in the first place?
what if the nodes are on a vibrating loop, then the nodes would = antinodes right?