EXERCISE HINTS: GETTING STARTED I'M STUCK! (a) Find the fundamental frequency and second harmonic if the tension in the wire is increased to 118 N. (Assume the wire doesn't stretch or break.) ffundamental Hz f2nd harmonic (b) Using a sound speed of 342 m/s, find the wavelengths of the sound waves produced. λ (larger) = m Hz λ (smaller) = m

College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
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)...
icon
Related questions
icon
Concept explainers
Question
SOLUTION
(A) Find the first three harmonics at the given tension.
Calculate the speed of the wave on the
wire:
Find the wire's fundamental frequency:
Find the next two harmonics by
multiplication:
F 1/2
80 N
= (-) ¹/² = ( 2.00 x 10-³ kg/m
V =
f₁
Substitute the values of F, μ, and L.
(B) Find the wavelength of the sound waves produced.
Solve = fλ for the wavelength and
substitute the frequencies.
f₂ = 2f₁ = 2.00 × 10² Hz, f3 = 3f₁:
=
V 2.00 x 10² m/s
2L 2(1.00 m)
(C) ind the fundamental frequency corresponding to the elastic limit.
Calculate the tension in the wire from
the elastic limit:
f₁
f₁
A₁ = v₁/f₁ = (345 m/s)/(1.00 x 10² Hz):
=
^₂ = vs/f₂ = (345 m/s)/(2.00 x 10² Hz) = 1.73 m
A₂ = v₁/f3 = (345 m/s)/(3.00 x 10² Hz) = 1.15 m
=
1
2L
F
== elastic limit → F = (elastic limit) A
A
F = (2.80 x 108 Pa) (2.56 x 10-7m²) = 71.7 N
1
2(1.00 m)
1/2
= 1.00 x 10² Hz
= 2.00 x 10² m/s
71.7 N
2.00 x 10-3 kg/m
·V.
3.00 x 10² Hz
3.45 m
94.7 Hz
Transcribed Image Text:SOLUTION (A) Find the first three harmonics at the given tension. Calculate the speed of the wave on the wire: Find the wire's fundamental frequency: Find the next two harmonics by multiplication: F 1/2 80 N = (-) ¹/² = ( 2.00 x 10-³ kg/m V = f₁ Substitute the values of F, μ, and L. (B) Find the wavelength of the sound waves produced. Solve = fλ for the wavelength and substitute the frequencies. f₂ = 2f₁ = 2.00 × 10² Hz, f3 = 3f₁: = V 2.00 x 10² m/s 2L 2(1.00 m) (C) ind the fundamental frequency corresponding to the elastic limit. Calculate the tension in the wire from the elastic limit: f₁ f₁ A₁ = v₁/f₁ = (345 m/s)/(1.00 x 10² Hz): = ^₂ = vs/f₂ = (345 m/s)/(2.00 x 10² Hz) = 1.73 m A₂ = v₁/f3 = (345 m/s)/(3.00 x 10² Hz) = 1.15 m = 1 2L F == elastic limit → F = (elastic limit) A A F = (2.80 x 108 Pa) (2.56 x 10-7m²) = 71.7 N 1 2(1.00 m) 1/2 = 1.00 x 10² Hz = 2.00 x 10² m/s 71.7 N 2.00 x 10-3 kg/m ·V. 3.00 x 10² Hz 3.45 m 94.7 Hz
13
=
(c) Suppose the wire is carbon steel with a density of 7.89 x 10³ kg/m³, a cross-sectional area A
= 2.68 x 10-7 m², and an elastic limit of 2.50 × 108 Pa. Find the fundamental frequency if the wire
is tightened to the elastic limit. Neglect any stretching of the wire (which would slightly reduce the
mass per unit length).
Hz
EXERCISE
HINTS: GETTING STARTED I I'M STUCK!
(a) Find the fundamental frequency and second harmonic if the tension in the wire is increased to 118 N.
(Assume the wire doesn't stretch or break.)
ffundamental
Hz
f2nd harmonic
342 237.69
X
Your response differs from the correct answer by more than 10%. Double check your
calculations. m
=
λ (smaller)
Hz
(b) Using a sound speed of 342 m/s, find the wavelengths of the sound waves produced.
λ (larger) =
m
m
Transcribed Image Text:13 = (c) Suppose the wire is carbon steel with a density of 7.89 x 10³ kg/m³, a cross-sectional area A = 2.68 x 10-7 m², and an elastic limit of 2.50 × 108 Pa. Find the fundamental frequency if the wire is tightened to the elastic limit. Neglect any stretching of the wire (which would slightly reduce the mass per unit length). Hz EXERCISE HINTS: GETTING STARTED I I'M STUCK! (a) Find the fundamental frequency and second harmonic if the tension in the wire is increased to 118 N. (Assume the wire doesn't stretch or break.) ffundamental Hz f2nd harmonic 342 237.69 X Your response differs from the correct answer by more than 10%. Double check your calculations. m = λ (smaller) Hz (b) Using a sound speed of 342 m/s, find the wavelengths of the sound waves produced. λ (larger) = m m
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps

Blurred answer
Knowledge Booster
Properties of sound
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
College Physics
College Physics
Physics
ISBN:
9781305952300
Author:
Raymond A. Serway, Chris Vuille
Publisher:
Cengage Learning
University Physics (14th Edition)
University Physics (14th Edition)
Physics
ISBN:
9780133969290
Author:
Hugh D. Young, Roger A. Freedman
Publisher:
PEARSON
Introduction To Quantum Mechanics
Introduction To Quantum Mechanics
Physics
ISBN:
9781107189638
Author:
Griffiths, David J., Schroeter, Darrell F.
Publisher:
Cambridge University Press
Physics for Scientists and Engineers
Physics for Scientists and Engineers
Physics
ISBN:
9781337553278
Author:
Raymond A. Serway, John W. Jewett
Publisher:
Cengage Learning
Lecture- Tutorials for Introductory Astronomy
Lecture- Tutorials for Introductory Astronomy
Physics
ISBN:
9780321820464
Author:
Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden
Publisher:
Addison-Wesley
College Physics: A Strategic Approach (4th Editio…
College Physics: A Strategic Approach (4th Editio…
Physics
ISBN:
9780134609034
Author:
Randall D. Knight (Professor Emeritus), Brian Jones, Stuart Field
Publisher:
PEARSON