Physics of Everyday Phenomena
Physics of Everyday Phenomena
9th Edition
ISBN: 9781259894008
Author: W. Thomas Griffith, Juliet Brosing Professor
Publisher: McGraw-Hill Education
bartleby

Concept explainers

bartleby

Videos

Textbook Question
Book Icon
Chapter 15, Problem 2SP

A guitar string has an overall length of 1.25 m and a total mass of 1.0 g (0.001 kg) before it is strung on the guitar. Once on the guitar, however, there is a distance of 69 cm between its fixed end points. It is tightened to a tension of 74 N.

a.    What is the mass per unit of length of this string?

b.    What is the wave speed for waves on the tightened string?

c.    What is the wavelength of the traveling waves that interfere to form the fundamental standing wave (nodes just at either end) for this string?

d.    What is the frequency of the fundamental wave?

e.    What are the wavelength and frequency of the next harmonic (with a node in the middle of the string)?

(a)

Expert Solution
Check Mark
To determine

The mass per unit length of the string.

Answer to Problem 2SP

The mass per unit length of the string is 8.0×104kg/m.

Explanation of Solution

Given Info: The length of the string is 1.25m and mass of the string is 0.001kg.

Write the expression to calculate the mass per unit length of the string.

μ=mL

Here,

μ is the mass per unit length of the string

L is the length of the string

m is the mass of the string

Substitute 1.25m for L and 0.001kg for m in the above equation to calculate μ.

μ=0.001kg1.25m=0.0008kg/m=8.0×104kg/m

Conclusion:

Therefore, the mass per unit length of the string is 8.0×104kg/m.

(b)

Expert Solution
Check Mark
To determine

The wave speed.

Answer to Problem 2SP

The wave speed is 304m/s.

Explanation of Solution

Given Info: The mass per unit length of the string is 0.0008kg/m and tension on the string is 74N.

Write the formula to calculate the wave speed.

v=Fμ

Here,

v is the wave speed

F is the tension on the string

Substitute 0.0008kg/m for μ and 74N for F in the above equation to calculate v.

v=74N0.0008kg/m304m/s

Conclusion:

Therefore, the wave speed is 304m/s.

(c)

Expert Solution
Check Mark
To determine

The wavelength of the travelling wave.

Answer to Problem 2SP

The wavelength is 1.38m.

Explanation of Solution

Given Info: The distance between two end is 69cm.

Write the expression to calculate the wavelength.

λ2=l

Here,

λ is the wavelength

l is the distance between two ends

Substitute 69cm for l in the above equation to calculate λ.

λ2=69cmλ=69cm(1m100cm)2=1.38m

Conclusion:

Therefore, the wavelength is 1.38m.

(d)

Expert Solution
Check Mark
To determine

The frequency of the standing wave.

Answer to Problem 2SP

The frequency of the standing wave is 220Hz.

Explanation of Solution

Given Info: The wavelength of the standing wave is The longest possible wavelength is 1.38m and speed is 304m/s.

Write the expression to calculate the speed of the sound wave.

v=fλ

Here,

λ is the wavelength of the standing wave which is longest possible wavelength

f is the frequency of the sound wave

Substitute 304m/s for v and 1.38m for λ in the above equation to calculate f.

f(1.38m)=304m/sf=304m/s1.38m220Hz

Conclusion:

Therefore, the frequency of the standing wave is 220Hz.

(e)

Expert Solution
Check Mark
To determine

The frequency and wavelength of the next harmonic wave.

Answer to Problem 2SP

The frequency of the second harmonic wave is 440Hz and wave length is 0.69m.

Explanation of Solution

Given Info: The distance between two end is 69cm and speed is 304m/s.

Write the formula to calculate the wavelength of the second harmonic.

λ=l

Here,

λ is the second harmonic wavelength.

Substitute 69cm for l in the above equation to calculate λ.

λ=69cm(1m100cm)=0.69m

Write the expression to calculate the speed of the sound wave.

v=fλ

Here,

f is the frequency of the second harmonic

Substitute 304m/s for v and 0.69m for λ in the above equation to calculate f.

f(0.69m)=304m/sf=304m/s0.69m440Hz

Conclusion:

Therefore, the frequency of the second harmonic wave is 440Hz and wave length is 0.69m.

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

Chapter 15 Solutions

Physics of Everyday Phenomena

Ch. 15 - Is it possible to produce a longitudinal wave on a...Ch. 15 - Suppose we double the mass per unit of length of a...Ch. 15 - Prob. 13CQCh. 15 - Prob. 14CQCh. 15 - Suppose we increase the tension in a rope, keeping...Ch. 15 - Is it possible for two waves traveling in the same...Ch. 15 - Prob. 17CQCh. 15 - Prob. 18CQCh. 15 - We can form standing waves on a rope attached to a...Ch. 15 - Prob. 20CQCh. 15 - Prob. 21CQCh. 15 - If we increase the tension of a guitar string,...Ch. 15 - Prob. 23CQCh. 15 - Prob. 24CQCh. 15 - Is it possible for sound to travel through a steel...Ch. 15 - Prob. 26CQCh. 15 - Prob. 27CQCh. 15 - Prob. 28CQCh. 15 - A band playing on a flat-bed truck is approaching...Ch. 15 - When the sound source is moving relative to the...Ch. 15 - Is it possible for sound waves to travel through a...Ch. 15 - Prob. 32CQCh. 15 - Prob. 33CQCh. 15 - What are we measuring when we perform a harmonic...Ch. 15 - How is the musical interval that we call a fifth...Ch. 15 - Prob. 36CQCh. 15 - Prob. 37CQCh. 15 - Two notes close together on the scale, such as do...Ch. 15 - Suppose that water waves coming into a dock have a...Ch. 15 - Suppose that water waves have a wavelength of 3.8...Ch. 15 - A longitudinal wave on a Slinky has a frequency of...Ch. 15 - Prob. 4ECh. 15 - A wave on a string has a speed of 11.5 m/s and a...Ch. 15 - Prob. 6ECh. 15 - A string with a length of 0.75 m is fixed at both...Ch. 15 - Suppose that the string in exercise 7 is plucked...Ch. 15 - Prob. 9ECh. 15 - What is the frequency of a sound wave with a...Ch. 15 - An organ pipe closed at one end and open at the...Ch. 15 - Suppose we start a major scale on concert A, which...Ch. 15 - If fa on a given scale has a frequency of 348 Hz,...Ch. 15 - Prob. 14ECh. 15 - If do has a frequency of 265 Hz and re a frequency...Ch. 15 - Prob. 16ECh. 15 - Prob. 17ECh. 15 - Prob. 1SPCh. 15 - A guitar string has an overall length of 1.25 m...Ch. 15 - A pipe that is open at both ends will form...Ch. 15 - For standard tuning, concert A is defined to have...Ch. 15 - Using the procedure outlined in section 15.5 where...
Knowledge Booster
Background pattern image
Physics
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
Text book image
University Physics Volume 1
Physics
ISBN:9781938168277
Author:William Moebs, Samuel J. Ling, Jeff Sanny
Publisher:OpenStax - Rice University
Text book image
Physics for Scientists and Engineers: Foundations...
Physics
ISBN:9781133939146
Author:Katz, Debora M.
Publisher:Cengage Learning
Text book image
College Physics
Physics
ISBN:9781938168000
Author:Paul Peter Urone, Roger Hinrichs
Publisher:OpenStax College
Text book image
Principles of Physics: A Calculus-Based Text
Physics
ISBN:9781133104261
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Text book image
Physics for Scientists and Engineers, Technology ...
Physics
ISBN:9781305116399
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Text book image
Physics for Scientists and Engineers with Modern ...
Physics
ISBN:9781337553292
Author:Raymond A. Serway, John W. Jewett
Publisher:Cengage Learning
Wave Speed on a String - Tension Force, Intensity, Power, Amplitude, Frequency - Inverse Square Law; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=vEzftaDL7fM;License: Standard YouTube License, CC-BY
Vibrations of Stretched String; Author: PhysicsPlus;https://www.youtube.com/watch?v=BgINQpfqJ04;License: Standard Youtube License