a) Sketch the standing wave patterns on a string for the four longest wavelengths for both sets of end conditions shown below. Beside each pattern, write the string-length-to-wavelength relationship.
a) Sketch the standing wave patterns on a string for the four longest wavelengths for both sets of end conditions shown below. Beside each pattern, write the string-length-to-wavelength relationship.
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Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Answers for FR-3 shown below.
Transcribed Image Text:'pəyp1ƏNs nok unued 2ARM
FR-3 a) Sketch the standing wave patterns on a string for the four longest wavelengths for both sets of end
conditions shown below. Beside each pattern, write the string-length-to-wavelength relationship.
HI
fixed
fixed
fixed
free
b) Start with V=Mf and the wavelength-to-string-length relationships from part a) and derive an expression
for f,/Af - the ratio of the frequency of the n" harmonic to the difference in frequency of adjacent
harmonics - for each of the two cases. The two strings are identical and have the same tension,
c) Given that a vibrating string has the sequential (adjacent) harmonics of 391HZ, 414HZ, and 437HZ,
use your results from b) to answer the following questions:
1. Is the string fixed-fixed or fixed-free?
2. What is the frequency of the first harmonic?
3. What are the harmonic numbers for the frequencies 391HZ, 414HZ, and 437HZ?
Answers
c) 210m/s d)52.5Hz, 158HZ, 263HZ, 368H(
FR-1 a)--- b) L=/4, L=3/4, L=5/4, L=7/4
FR-2 a)--- b) L=A, L=22, L=31 c) 512HZ, 1,024HZ1.02x10 Hz, 1,535HZ1,54x10°Hz
FR-3 a) Fixed-fixed: L=/2, L-1, L=3/2, L=22 Fixed-free: L=/4, L-3/4, L-52/4, L=7A/4
b) Fixed-fixed: f„/Af=n, Fixed-free: f,/Af=n/2
c) 1. Fixed-fixed 2. 23HZ 3. n-17, 18, 19
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