University Physics Volume 1
18th Edition
ISBN: 9781938168277
Author: William Moebs, Samuel J. Ling, Jeff Sanny
Publisher: OpenStax - Rice University
expand_more
expand_more
format_list_bulleted
Concept explainers
Textbook Question
Chapter 16, Problem 106P
Consider a rod of length L, mounted in the center to a support. A node must exist where the rod is mounted on a support, as shown below. Draw the first two normal modes of the rod as it is driven into resonance. Label the wavelength and the frequency required to drive the rod into resonance.
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
Consider a rod of length L, mounted in the center to a support. A node must exist where the rod is mounted on a support, as shown below. Draw the first two normal modes of the rod as it is driven into resonance. Label the wavelength and the frequency required to drive the rod into resonance.
Problem 2
Let y1
equal amplitude, traveling in opposite directions.
a) Using the trig identity
A sin(kx – wt) and y2 = A sin(kx + wt) represent two waves of
sin(a +b) = sin(a) cos(b) ± cos(a) sin(b),
compute the resultant wave y = y1 + yY2.
b) If y(x = 0) = 0 and y(x = L) = 0, what is the form of the wavevector k?
c) What type of wave is described in this problem?
d) If L = 4, what are the allowed wavelengths?
%3D
Consider the system formed by four bodies on
a horizontal rope embedded at both ends, as shown in the figure. Consider the corresponding approximations for each component of the system to describe
a simple harmonic motion vertically around the embedment height of the string. The tension in the string is uniform and
equal to T, the four masses are equal to m and the distance
between the embedment points and the suspended body
is d.
a) Solve the normal modes problem and find the four normal frequencies of oscillation and the
corresponding amplitudes in which each
component.
Chapter 16 Solutions
University Physics Volume 1
Ch. 16 - Check Your Understanding When a guitar string is...Ch. 16 - Check Your Understanding The propagation velocity...Ch. 16 - Check Your Understanding The wave function above...Ch. 16 - Check Your Understanding The wave equation...Ch. 16 - Check Your Understanding The wave speed of a wave...Ch. 16 - Check Your Understanding Is the time-averaged...Ch. 16 - Check Your Understanding The equations for the...Ch. 16 - Give one example of a transverse wave and one...Ch. 16 - A sinusoidal transverse wave has a wavelength of...Ch. 16 - What is the difference between propagation speed...
Ch. 16 - Consider a stretched spring, such as a slinky. The...Ch. 16 - Consider a wave produced on a stretched spring by...Ch. 16 - A sinusoidal, transverse wave is produced on a...Ch. 16 - An electromagnetic wave, such as light, does not...Ch. 16 - If you were to shake the end of a taut spring up...Ch. 16 - If you shake the end of a stretched spring up and...Ch. 16 - Does the vertical speed of a segment of a...Ch. 16 - In this section, we have considered waves that...Ch. 16 - If you drop a pebble in a pond you may notice that...Ch. 16 - If the tension in a string were increased by a...Ch. 16 - Does a sound wave move faster in seawater or fresh...Ch. 16 - Guitars have strings of different linear mass...Ch. 16 - Shown below are three waves that were sent down a...Ch. 16 - Electrical power lines connected by two utility...Ch. 16 - Two strings, one with a low mass density and one...Ch. 16 - Consider a string with under tension with a...Ch. 16 - Circular water waves decrease in amplitude as they...Ch. 16 - In a transverse wave on a string, the motion of...Ch. 16 - The energy from the sun warms the portion of the...Ch. 16 - The intensity of a spherical waves decreases as...Ch. 16 - An incident sinusoidal wave is sent along a string...Ch. 16 - A string of a length of 2.00 m with a linear mass...Ch. 16 - A long, tight spring is held by two students, one...Ch. 16 - Many of the topics discussed in this chapter are...Ch. 16 - A string of a constant linear mass density is held...Ch. 16 - A truck manufacturer finds that a strut in the...Ch. 16 - Why do roofs of gymnasiums and churches seem to...Ch. 16 - Wine glasses can be set into resonance by...Ch. 16 - Air conditioning units are sometimes placed on the...Ch. 16 - Consider a standing wave modeled as...Ch. 16 - Storms in the South Pacific can create waves that...Ch. 16 - Waves on a swimming pool propagate at 0.75 m/s....Ch. 16 - Wind gusts create ripples on the ocean that have a...Ch. 16 - How many times a minute does a boat bob up and...Ch. 16 - Scouts at a camp shake the rope bridge they have...Ch. 16 - What is the wavelength of the waves you create in...Ch. 16 - What is the wavelength of an earthquake that...Ch. 16 - Radio waves transmitted through empty space at the...Ch. 16 - Your ear is capable of differentiating sounds that...Ch. 16 - (a) Seismographs measure the arrival times of...Ch. 16 - A Girl Scout is taking a 10.00-km hike to earn a...Ch. 16 - A quality assurance engineer at a frying pan...Ch. 16 - A pulse can be described as a single wave...Ch. 16 - A transverse wave on a string is modeled with the...Ch. 16 - Consider the wave function...Ch. 16 - A pulse is defined as y(x,t)=e2.77( 2.00( x2.00m/s...Ch. 16 - A wave is modeled at time t=0.00s with a wave...Ch. 16 - A wave is modeled with the function...Ch. 16 - A surface ocean wave has an amplitude of 0.60 m...Ch. 16 - A wave is modeled by the wave function...Ch. 16 - A transverse wave on a string is described with...Ch. 16 - A swimmer in the ocean observes one day that the...Ch. 16 - Consider a wave described by the wave function...Ch. 16 - Consider two waves defined by the wave functions...Ch. 16 - Consider two waves defined by the wave functions...Ch. 16 - The speed of a transverse wave on a string is...Ch. 16 - Transverse waves are sent along a 5.00-m-long...Ch. 16 - A copper wire has a density of =8920 kg/m3, a...Ch. 16 - A piano wire has a linear mass density of =4.95103...Ch. 16 - A string with a linear mass density of =0.0060...Ch. 16 - A cord has a linear mass density of =0.0075 kg/m...Ch. 16 - A string is 3.00 m long with a mass of 5.00 g. The...Ch. 16 - Two strings are attached to poles, however the...Ch. 16 - Two strings are attached to poles, however the...Ch. 16 - Transverse waves travel through a string where the...Ch. 16 - Two strings are attached between two poles...Ch. 16 - Two strings are attached between two poles...Ch. 16 - The note E4 is played on a piano and has a...Ch. 16 - Two transverse waves travel through a taut string....Ch. 16 - A sinusoidal wave travels down a taut, horizontal...Ch. 16 - The speed of a transverse wave on a string is...Ch. 16 - A string of length 5 m and a mass of 90 g is held...Ch. 16 - Ultrasound of intensity 1.50102W/m2 is produced by...Ch. 16 - The low-frequency speaker of a stereo set has...Ch. 16 - To increase the intensity of a wave by a factor of...Ch. 16 - A device called an insolation meter is used to...Ch. 16 - Energy from the Sun arrives at the top of Earth’s...Ch. 16 - Suppose you have a device that extracts energy...Ch. 16 - A photovoltaic array of (solar cells) is 10.0%...Ch. 16 - A microphone receiving a pure sound tone feeds an...Ch. 16 - A string with a mass of 0.30 kg has a length of...Ch. 16 - The power versus time for a point on a string...Ch. 16 - A string is under tension FT1. Energy is...Ch. 16 - A 250-Hz tuning fork is struck and the intensity...Ch. 16 - A sound speaker is rated at a voltage of P=120.00...Ch. 16 - The energy of a ripple on a pond is proportional...Ch. 16 - Consider two sinusoidal waves traveling along a...Ch. 16 - Consider two sinusoidal sine waves traveling along...Ch. 16 - Consider two sinusoidal sine waves traveling along...Ch. 16 - Two sinusoidal waves are moving through a medium...Ch. 16 - Two sinusoidal waves are moving through a medium...Ch. 16 - Two sinusoidal waves are moving through a medium...Ch. 16 - Consider two waves y1(x,t) and y2(x,t) that are...Ch. 16 - Two sinusoidal waves, which are identical except...Ch. 16 - Two sinusoidal waves, which are identical except...Ch. 16 - Consider two wave functions,...Ch. 16 - Consider two wave functions,...Ch. 16 - Consider two wave functions that differ only by a...Ch. 16 - A wave traveling on a Slinky® that is stretched to...Ch. 16 - A 2-m long string is stretched between two...Ch. 16 - Consider the experimental setup shown below. The...Ch. 16 - A cable with a linear density of =0.2 kg/m is hung...Ch. 16 - Consider a rod of length L, mounted in the center...Ch. 16 - Consider two wave functions...Ch. 16 - A 2.40-m wire has a mass of 7.50 g and is under a...Ch. 16 - A string with a linear mass density of 0.0062 kg/m...Ch. 16 - A string with a linear mass density of 0.0075 kg/m...Ch. 16 - Two sinusoidal waves with identical wavelengths...Ch. 16 - A string, fixed on both ends, is 5.00 m long and...Ch. 16 - A string is fixed at both end. The mass of the...Ch. 16 - The frequencies of two successive modes of...Ch. 16 - A string is fixed at both ends to supports 3.50 m...Ch. 16 - Sine waves are sent down a 1.5-m-long string fixed...Ch. 16 - Ultrasound equipment used in the medical...Ch. 16 - Shown below is the plot of a wave function that...Ch. 16 - The speed of light in air is approximately...Ch. 16 - A radio station broadcasts radio waves at a...Ch. 16 - A sunbather stands waist deep in the ocean and...Ch. 16 - A tuning fork vibrates producing sound at a...Ch. 16 - A motorboat is traveling across a lake at a speed...Ch. 16 - Use the linear wave equation to show that the wave...Ch. 16 - Given the wave functions y1(x,t)=Asin(kxt) and...Ch. 16 - A transverse wave on a string is modeled with the...Ch. 16 - A sinusoidal wave travels down a taut, horizontal...Ch. 16 - A transverse wave on a string (=0.0030kg/m) is...Ch. 16 - A transverse wave on a horizontal string...Ch. 16 - A student holds an inexpensive sonic range finder...Ch. 16 - A wave on a string is driven by a string vibrator,...Ch. 16 - A traveling wave on a string is modeled by the...Ch. 16 - A transverse wave on a string has a wavelength of...Ch. 16 - (a) What is the intensity of a laser beam used to...Ch. 16 - Consider two periodic wave functions,...Ch. 16 - Consider two periodic wave functions,...Ch. 16 - A trough with dimensions 10.00 meters by 0.10...Ch. 16 - A seismograph records the S- and P-waves from an...Ch. 16 - Consider what is shown below. A 20.00-kg mass...Ch. 16 - Consider the superposition of three wave functions...Ch. 16 - A string has a mass of 150 g and a length of 3.4...Ch. 16 - A standing wave is produced on a string under a...Ch. 16 - A string with a length of 4 m is held under a...Ch. 16 - A copper wire has a radius of 200 µ m and a length...Ch. 16 - A pulse moving along the x axis can be modeled as...Ch. 16 - A string with a linear mass density of =0.0085...Ch. 16 - Consider two wave functions y1(x,t)=Asin(kxt) and...Ch. 16 - The wave function that models a standing wave is...Ch. 16 - Consider two wave functions y1(x,t)=Asin(kxt) and...
Additional Science Textbook Solutions
Find more solutions based on key concepts
5. Why must a room air conditioner be placed in a window rather than just set on the floor and plugged in? Why ...
College Physics (10th Edition)
37. Two common metric units of volume are ______ and ______.
Applied Physics (11th Edition)
Your 200-g cup of tea is boiling-hot. About how much ice should you add to bring it down to a comfortable sippi...
An Introduction to Thermal Physics
3. What is free-fall, and why does it make you weightless? Briefly describe why astronauts are weightless in th...
The Cosmic Perspective
Prove that if I is the intensity of light transmitted by two polarizing filters with axes at an angle and I’ is...
University Physics Volume 3
3. What is free-fall, and why does it make you weightless? Briefly describe why astronauts are weightless in th...
The Cosmic Perspective (8th Edition)
Knowledge Booster
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
- A violin string of L=31.8 cm in length and u=0.64gm/linear mass density is tuned to play an A4 note at 440.0 Hz. This means that the string is in its fundamental oscillation mode, i.e., it will be on that note without placing any fingers on it. From this information, Calculate the tension on the string that allows it to be kept in tune. B. If from the midpoint of the string a maximum transverse motion 2.59 mm is observed when it is in the fundamental mode, what is the maximum speed vy máx of the string's antinode? C. If the string tension is reduced by 6.3% of the tension found in A, what is the resulting frequency of the note produced? D. When playing violin different notes can be produced depending on the position of the fingers of one hand on the string. The usual technique presses the string hard against the fingerboard, reducing the length of the string that can vibrate. If we consider this string initially tuned to an A4, and a finger is placed one third of the length down from…arrow_forwardA first order instrument with a time constant of 1.5 seconds is to be used to measure a periodic input. A dynamic error of 2% can be tolerated. The maximum frequency of periodic input that can be measured (rad) Select one: a. 0.1353 b. 1.529 c. 0.1035 d. 1.659arrow_forwardThe provided image shows vibrations from a car idle at 33 Hz. The fourier transform of the data is shown in the bottom plot. Are the following statements true or false? A fourier series that would represent the vibrational data would contain two frequences of 15 Hz and 30 Hz. This data has a vibrational noise at a fundamental frequency of 15 Hz as well as the three overtones to this fundamental. The oscillations seen in the data are due to the vibrational noise at 15 Hz and 30 Hz.arrow_forward
- Suppose that a spacecraft near Neptune has measured a quantity A and sent it to earth in the form of a periodic signal A cost of amplitude A. On its way to earth, the signal picks up periodic noise, containing only second and higher harmonics. Suppose that the signal h(t) actually received on earth is graphed below. 10 -pi -pi/2 pi/2 pi -10 Determine the signal that the spacecraft originally sent and hence the value A of the measurement. A = -60arrow_forwardIn the figure it is desirable to determine the natural frequencies, the shape of the modes and the response of the system if x(0) = 1 . Slender bar of mass m m Tearrow_forwardProblem 7: Derive the wave equation for a sinusoidal wave function.arrow_forward
- Say that a string with linear mass density of 3 g/m is connected to a mechanical oscillator on the left end and sent over a pulley on the right, as shown. A mass of 0.50 kg is hung from the string, and the mass remains stationary. The distance between the oscillator and the pulley, which can both be treated as fixed ends, is 2.0 m. What is the wavelength of the fundamental mode? M O1 m 2 m 4 m 8 marrow_forward(a) At what displacement of a SHO is the energy half kinetic and half potential? (b) What fraction of the total energy of a SHO is kinetic and what fraction potential when the displacement is one third the amplitude? Sketch the scenario. List the formulas needed and explain how it relates to the situation. Solve for the algebraic expressionsarrow_forwardA wire is under tension due to hanging mass. The observed wave speed is 24 m/s when the suspended mass is 3kg. a) what is the string's linear density ? b) if the length of the vibrating portion of the string is 1.2m, what is the frequency?arrow_forward
- For the arrangement shown below, the inclined plane and the small pulley are frictionless; the string supports the object of mass M at the bottom of the plane; and the string has mass m. The system is in equilibrium, and the vertical part of the string has a length h. We wish to study standing waves set up on the vertical section of the string. h M (a) What analysis model describes the object of mass M? particle under constant acceleration model nonisolated system model rigid object in equilibrium model waves under boundary conditions model particle in simple harmonic motion model (b) What analysis model describes the waves on the vertical part of the string? particle in simple harmonic motion model O particle under constant acceleration model waves under boundary conditions model O waves in interference model O rigid object in equilibrium model (c) Find the tension in the string. (Use any variable or symbol stated above along with the following as necessary: g.) T = (d) Model the…arrow_forwardA wave is modeled by the wave function: y (x, t) = A sin [ 2π/0.1 m (x - 12 m/s*t)] 1. Find the wavelength, wave number, wave velocity, period and wave frequency. 2. Construct on the computer, in the same graph, the dependence of y (x, t) from x on t = 0 and t = 5 s in case the value of amplitude A corresponds to the first letter of your name: letter E A. A=0.1 mB. A=0.15 mC. A=0.2 mÇ. A=0.25 mD. A=0.3 mDh. A=0.35 mE. A=0.4 mË. A=0.45 mF. A=0.5 m G. A=0.55 mGj. A=0.6 mH. A=0.65 mI. A=0.7 mJ. A=0.75 mK. A=0.8 mL. A=0.85 mLl. A=0.9 mM. A=0.95 m N. A=1.05 mNj. A= 1.1 mO. A=1.15 mP. A=1.2 mQ. A=1.25 mR. A=1.3 mRr. A=1.35 mS. A=1.4 mSh. A=1.45 m T. A=1.5 mTh. A=1.55 mU. A=1.6 mV. A=1.65 mX. A=1.7 mXh. A=1.75 mY. A=1.8 mZ. A=1.85 mZh. A=1.9 m 3. After constructing the graph, make the appropriate interpretations and comments from the result that you got graphically. 4. How much is the wave displaced during the time interval from t = 0 to t = 5 s? Does it match this with the graph results?…arrow_forwardTwo masses are hanging from a steel wire of mass 60gas shown. A wave pulse travels along the wire from point1 to point 2 in 24ms. What is the mass m?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- Classical Dynamics of Particles and SystemsPhysicsISBN:9780534408961Author:Stephen T. Thornton, Jerry B. MarionPublisher:Cengage Learning
Classical Dynamics of Particles and Systems
Physics
ISBN:9780534408961
Author:Stephen T. Thornton, Jerry B. Marion
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