The document discusses standing waves on a string. It provides examples of calculating the mass hanging on the end of a string, the maximum mass that can be used to still create a coherent standing wave pattern for a fixed frequency, and the fundamental frequency and wave speed for standing waves on a string fixed at both ends showing successive frequencies. It also gives an example of calculating the frequency of a wave source based on the time it takes the wave to travel a given distance and the number of complete loops observed.
This LO gives you a simple easy to understand explanation of what a standing wave is (video included) and how it is different from a travelling wave. Afterwards a few sample questions are given to apply knowledge.
Learning Object- Standing Waves on Stringskendrick24
This is my learning object about standing waves on a string. I talk about the harmonics, the equation for calculating the frequency for a wave on a string, and gave an example problem.
This LO gives you a simple easy to understand explanation of what a standing wave is (video included) and how it is different from a travelling wave. Afterwards a few sample questions are given to apply knowledge.
Learning Object- Standing Waves on Stringskendrick24
This is my learning object about standing waves on a string. I talk about the harmonics, the equation for calculating the frequency for a wave on a string, and gave an example problem.
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In this presentation, I explain what a standing wave on a string is, the difference between a standing wave and a travelling wave, and go over some practice problems.
Using the violin, I posed word problems that enforce the concepts of a standing wave and illustrate how to apply the equations related to standing waves. I provided the solutions and explanations of my problems.
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Bio
Dr. Michel Dumontier is the Distinguished Professor of Data Science at Maastricht University, founder and executive director of the Institute of Data Science, and co-founder of the FAIR (Findable, Accessible, Interoperable and Reusable) data principles. His research explores socio-technological approaches for responsible discovery science, which includes collaborative multi-modal knowledge graphs, privacy-preserving distributed data mining, and AI methods for drug discovery and personalized medicine. His work is supported through the Dutch National Research Agenda, the Netherlands Organisation for Scientific Research, Horizon Europe, the European Open Science Cloud, the US National Institutes of Health, and a Marie-Curie Innovative Training Network. He is the editor-in-chief for the journal Data Science and is internationally recognized for his contributions in bioinformatics, biomedical informatics, and semantic technologies including ontologies and linked data.
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This pdf is about the Schizophrenia.
For more details visit on YouTube; @SELF-EXPLANATORY;
https://www.youtube.com/channel/UCAiarMZDNhe1A3Rnpr_WkzA/videos
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1. Left
Most of the vibrations cancel each other out but only ones that lead to standing waves survive.
Right
Note the relationship between the string’s wavelength (lambda) and its length.
(https://sites.google.com/site/bromfieldphysics/waves)
2. Long answerquestions – Standing waves on a string
1. A standing wave pattern is created on a string with mass density μ = 0.00049 kg/m. A
wave generator with frequency f = 33 Hz is attached to one end of the string and the
other end goes over a pulley and is connected to a mass (weight of the string between
the pulley and mass is ignored). The distance between the generator and pulley is L=
0.52 m. Initially the 3rd harmonic wave pattern
wavelength = 0.337 m
speed of wave = 11.121 m/sec
tension = 0.215N
(1) What is the mass hanging on the end of the string?
(2) Keeping the frequency fixed at f = 61 Hz, what is the maximum mass that
can be used to still create a coherent standing wave pattern?
A. The gravity force on the mass supplies the tension
m . g = 0.215
m = 0.215/9.81
m = 0.0219 kg (21.9g)
Increasing the mass -> increase the tension -> increase the velocity
with the fixed frequency -> wavelength must increase
The maximum wavelength(2L) possible is 1.04 m
so the maximum speed to produce a coherent standing wave
= 33*1.04 = 34.32m/s
34.32 = √ T / 0.00049
T = (34.32)^2 * 0.00049
= 0.577152576N = 0.5772N
M (max) = T / g = 0.0588 kg = 58.8 g
2. Standing waves on a 1.2m long string that is fixed at both ends are seen at successive
frequencies of 35 Hz and 70 Hz.
(1) What is the fundamental frequency?
(2) What is the wave speed?
A. The ratio of frequencies = ratio of frequencies as in the case of open organ pipe.
n1 = 35Hz n2 = 70Hz = 2*n1
fundamental frequency = n1 = 35 Hz.
1/2wavelength=1.2 m. wavelength=2.4m.
velocity = frequency * wavelength = 35*2.4 = 84.0 m/s.
Fundamental frequency = 35Hz
Wave velocity = 84.0 m/s
3. A string has one end tied to a wave generator, and the other tied to a fixed position. It
takes the wave 0.13s to travel 3.8m. Within the same distance, there are two complete
loops. What is the frequency of the source?
A. Each loop has 0.5 wavelengths, and there are 2 loops
in total, there are 1.0 complete wavelength in 3.8m.
3.8m / 1.0 = 3.8 so the wavelength lambda = 3.8
3. speed of wave c = frequency x wavelength
speed of wave c = d / t = 3.8 / 0.13 = 29.23m/s
so frequency f = c / lambda
f = 29.23 / 3.8 = 7.69
frequency f = 7.69Hz
