Concept explainers
Videos
A pipe that is open at both ends will form standing waves, if properly excited, with antinodes near both ends of the pipe. Suppose we have an open pipe 60 cm in length.
a. Sketch the standing-wave pattern for the fundamental standing wave for this pipe. (There will be a node in the middle, and antinodes at either end.)
b. What is the wavelength of the sound waves that interfere to form the fundamental wave?
c. If the speed of sound in air is 340 m/s, what is the frequency of this sound wave?
d. If the air temperature increases so that the speed of sound is now 358 m/s. by how much does the frequency change?
e. Sketch the standing-wave pattern and find the wavelength and frequency for the next harmonic in this pipe.
(a)
Sketch the sound-wave pattern for this pipe.
Answer to Problem 3SP
The fundamental wave pattern in the pipe is drawn.
Explanation of Solution
Conclusion:
Therefore, the fundamental sound-wave pattern is drawn.
(b)
The wavelength of the sound wave.
Answer to Problem 3SP
The wavelength is
Explanation of Solution
Given Info: The length of the pipe is
Write the formula to calculate the fundamental wavelength inside the pipe.
Here,
L is the length of the pipe
Substitute
Conclusion:
Therefore, the wavelength is
(c)
The frequency of the sound wave.
Answer to Problem 3SP
The frequency of the sound wave is
Explanation of Solution
Given Info: The wavelength of the sound wave is
Write the expression to calculate the speed of the sound wave.
Here,
f is the frequency of the sound wave
Substitute
Conclusion:
Therefore, the frequency of the sound wave is
(d)
The change in frequency of the sound wave.
Answer to Problem 3SP
The change in frequency of the sound wave is
Explanation of Solution
Given Info: The wavelength of the sound wave is The longest possible wavelength is
Write the expression to calculate the speed of the sound wave.
Here,
Substitute
Write the formula to calculate the frequency change for the sound wave.
Here,
Substitute
Conclusion:
Therefore, the change in frequency of the sound wave is
(e)
Sketch the standing-wave pattern for the next harmonic and find wavelength and frequency.
Answer to Problem 3SP
The frequency of the second harmonic wave is
Explanation of Solution
For the second harmonic, the frequency is twice as that of the fundamental standing-wave and wavelength is half of that value of the fundamental standing wave. Therefore the frequency of the second harmonic wave is
The sketch of the second harmonic wave is shown below.
Conclusion:
Therefore, the frequency of the second harmonic wave is
Want to see more full solutions like this?
Chapter 15 Solutions
Physics of Everyday Phenomena
- For each of the actions depicted below, a magnet and/or metal loop moves with velocity v→ (v→ is constant and has the same magnitude in all parts). Determine whether a current is induced in the metal loop. If so, indicate the direction of the current in the loop, either clockwise or counterclockwise when seen from the right of the loop. The axis of the magnet is lined up with the center of the loop. For the action depicted in (Figure 5), indicate the direction of the induced current in the loop (clockwise, counterclockwise or zero, when seen from the right of the loop). I know that the current is clockwise, I just dont understand why. Please fully explain why it's clockwise, Thank youarrow_forwardA planar double pendulum consists of two point masses \[m_1 = 1.00~\mathrm{kg}, \qquad m_2 = 1.00~\mathrm{kg}\]connected by massless, rigid rods of lengths \[L_1 = 1.00~\mathrm{m}, \qquad L_2 = 1.20~\mathrm{m}.\]The upper rod is hinged to a fixed pivot; gravity acts vertically downward with\[g = 9.81~\mathrm{m\,s^{-2}}.\]Define the generalized coordinates \(\theta_1,\theta_2\) as the angles each rod makes with thedownward vertical (positive anticlockwise, measured in radians unless stated otherwise).At \(t=0\) the system is released from rest with \[\theta_1(0)=120^{\circ}, \qquad\theta_2(0)=-10^{\circ}, \qquad\dot{\theta}_1(0)=\dot{\theta}_2(0)=0 .\]Using the exact nonlinear equations of motion (no small-angle or planar-pendulumapproximations) and assuming the rods never stretch or slip, determine the angle\(\theta_2\) at the instant\[t = 10.0~\mathrm{s}.\]Give the result in degrees, in the interval \((-180^{\circ},180^{\circ}]\).arrow_forwardWhat are the expected readings of the ammeter and voltmeter for the circuit in the figure below? (R = 5.60 Ω, ΔV = 6.30 V) ammeter I =arrow_forward
- simple diagram to illustrate the setup for each law- coulombs law and biot savart lawarrow_forwardA circular coil with 100 turns and a radius of 0.05 m is placed in a magnetic field that changes at auniform rate from 0.2 T to 0.8 T in 0.1 seconds. The plane of the coil is perpendicular to the field.• Calculate the induced electric field in the coil.• Calculate the current density in the coil given its conductivity σ.arrow_forwardAn L-C circuit has an inductance of 0.410 H and a capacitance of 0.250 nF . During the current oscillations, the maximum current in the inductor is 1.80 A . What is the maximum energy Emax stored in the capacitor at any time during the current oscillations? How many times per second does the capacitor contain the amount of energy found in part A? Please show all steps.arrow_forward
- A long, straight wire carries a current of 10 A along what we’ll define to the be x-axis. A square loopin the x-y plane with side length 0.1 m is placed near the wire such that its closest side is parallel tothe wire and 0.05 m away.• Calculate the magnetic flux through the loop using Ampere’s law.arrow_forwardDescribe the motion of a charged particle entering a uniform magnetic field at an angle to the fieldlines. Include a diagram showing the velocity vector, magnetic field lines, and the path of the particle.arrow_forwardDiscuss the differences between the Biot-Savart law and Coulomb’s law in terms of their applicationsand the physical quantities they describe.arrow_forward
- Explain why Ampere’s law can be used to find the magnetic field inside a solenoid but not outside.arrow_forward3. An Atwood machine consists of two masses, mA and m B, which are connected by an inelastic cord of negligible mass that passes over a pulley. If the pulley has radius RO and moment of inertia I about its axle, determine the acceleration of the masses mA and m B, and compare to the situation where the moment of inertia of the pulley is ignored. Ignore friction at the axle O. Use angular momentum and torque in this solutionarrow_forwardA 0.850-m-long metal bar is pulled to the right at a steady 5.0 m/s perpendicular to a uniform, 0.650-T magnetic field. The bar rides on parallel metal rails connected through a 25-Ω, resistor (Figure 1), so the apparatus makes a complete circuit. Ignore the resistance of the bar and the rails. Please explain how to find the direction of the induced current.arrow_forward
Glencoe Physics: Principles and Problems, Student...PhysicsISBN:9780078807213Author:Paul W. ZitzewitzPublisher:Glencoe/McGraw-Hill
University Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice University
Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning
Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning
College PhysicsPhysicsISBN:9781938168000Author:Paul Peter Urone, Roger HinrichsPublisher:OpenStax College
Physics for Scientists and Engineers, Technology ...PhysicsISBN:9781305116399Author:Raymond A. Serway, John W. JewettPublisher:Cengage Learning