1 Physics And Measurement 2 Motion In One Dimension 3 Vectors 4 Motion In Two Dimensions 5 The Laws Of Motion 6 Circular Motion And Other Applications Of Newton’s Laws 7 Energy Of A System 8 Conservation Of Energy 9 Linear Momentum And Collisions 10 Rotation Of A Rigid Object About A Fixed Axis 11 Angular Momentum 12 Static Equilibrium And Elasticity 13 Universal Gravitation 14 Fluid Mechanics 15 Oscillatory Motion 16 Wave Motion 17 Sound Waves 18 Superposition And Standing Waves 19 Temperature 20 The First Law Of Thermodynamics 21 The Kinetic Theory Of Gases 22 Heat Engines, Entropy, And The Second Law Of Thermodynamics 23 Electric Fields 24 Gauss’s Law 25 Electric Potential 26 Capacitance And Dielectrics 27 Current And Resistance 28 Direct-current Circuits 29 Magnetic Fields 30 Sources Of The Magnetic Field 31 Faraday’s Law 32 Inductance 33 Alternating Current Circuits 34 Electromagnetic Waves 35 The Nature Of Light And The Principles Of Ray Optics 36 Image Formation 37 Wave Optics 38 Diffraction Patterns And Polarization 39 Relativity Chapter18: Superposition And Standing Waves
Chapter Questions Section: Chapter Questions
Problem 18.1QQ Problem 18.2QQ: Consider the waves in Figure 17.8 to be waves on a stretched string. Define the velocity of elements... Problem 18.3QQ: When a standing wave is set up on a string fixed at both ends, which of the following statements is... Problem 18.4QQ Problem 18.5QQ: Balboa Park in San Diego has an outdoor organ. When the air temperature increases, the fundamental... Problem 18.1OQ: In figure OQ18.1 (page 566), a sound wave of wave-lenght 0.8 m divides into two equal parts that... Problem 18.2OQ: A string of length L, mass pet unit length , and tension T is vibrating at its fundamental... Problem 18.3OQ: In Example 18.1, we investigated an oscillator at 1.3kHz driving two identical side-by-side... Problem 18.4OQ Problem 18.5OQ: A flute has a length of 58.0 cm. If the speed of sound in air is 343 m/s, what is the fundamental... Problem 18.6OQ: When two tuning forks are sounded at the same time, a beat frequency of 5 Hz occurs. If one of the... Problem 18.7OQ: A tuning fork is known to vibrate with frequency 262 Hz. When it is sounded along with a mandolin... Problem 18.8OQ: An archer shoots an arrow horizontally from the center of the string of a bow held vertically. Alter... Problem 18.9OQ: As oppositely moving pulses of the same shape (one upward, one downward) on a string pass through... Problem 18.10OQ Problem 18.11OQ: Suppose all six equal-length strings of an acoustic guitar are played without fingering, that is,... Problem 18.12OQ: Assume two identical sinusoidal waves are moving through the same medium in the same direction.... Problem 18.1CQ Problem 18.2CQ: When two waves interfere constructively or destructively, is there any gain or loss in energy in the... Problem 18.3CQ Problem 18.4CQ: What limits the amplitude of motion of a real vibrating system that is driven at one of its resonant... Problem 18.5CQ Problem 18.6CQ: An airplane mechanic notices that the sound from a twin-engine aircraft rapidly varies in loudness... Problem 18.7CQ: Despite a reasonably steady hand, a person often spills his coffee when carrying it to his seal.... Problem 18.8CQ Problem 18.9CQ: Does the phenomenon of wave interference apply only to sinusoidal waves? Problem 18.1P: Two waves are traveling in the same direction along a stretched string. The waves are 90.0 out of... Problem 18.2P: Two wave pulses A and B are moving in opposite directions, each with a speed v = 2.00 cm/s. The... Problem 18.3P: Two waves on one string are described by the wave functions y1=3.0cos(4.0x1.6t)y2=4.0sin(5.0x2.0)t... Problem 18.4P: Two pulses of different amplitudes approach each other, each having a speed of v = 1.00 m/s. Figure... Problem 18.5P: A tuning fork generates sound waves with a frequency of 246 Hz. The waves travel in opposite... Problem 18.6P: The acoustical system shown in Figure OQ18.1 is driven by a speaker emitting sound of frequency 756... Problem 18.7P: Two pulses traveling on the same string are described by y1=5(3x4t)2+2y2=5(3x+4t6)2+2 (a) In which... Problem 18.8P: Two identical loudspeakers are placed on a wall 2.00 m apart. A listener stands 3.00 m from the wall... Problem 18.9P: Two traveling sinusoidal waves are described by the wave functions y1 = 5.00 sin [(4.00x 1 200t)]... Problem 18.10P: Why is the following situation impossible? Two identical loudspeakers are driven by the same... Problem 18.11P: Two sinusoidal waves on a string are defined by the wave functions... Problem 18.12P: Two identical sinusoidal waves with wavelengths of 3.00 m travel in the same direction at a speed of... Problem 18.13P: Two identical loudspeakers 10.0 m apart are driven by the same oscillator with a frequency of f =... Problem 18.14P Problem 18.15P: Two sinusoidal waves traveling in opposite directions interfere to produce a standing wave with the... Problem 18.16P: Verify by direct substitution that the wave function for a standing wave given in Equation 17.1,... Problem 18.17P: Two transverse sinusoidal waves combining in a medium are described by the wave functions y1 = 3.00... Problem 18.18P: A standing wave is described by the wave function y=6sin(2x)cos(100t) where x and y are in meters... Problem 18.19P: Two identical loudspeakers are driven in phase by a common oscillator at 800 Hz and face each other... Problem 18.20P Problem 18.21P: A string with a mass m = 8.00 g and a length L = 5.00 m has one end attached to a wall; the other... Problem 18.22P: The 64.0-cm-long string of a guitar has a fundamental frequency of 330 Hz when it vibrates freely... Problem 18.23P: The A string on a cello vibrates in its first normal mode with a frequency of 220 Hz. The vibrating... Problem 18.24P: A taut string has a length of 2.60 m and is fixed at both ends. (a) Find the wavelength of the... Problem 18.25P: A certain vibrating string on a piano has a length of 74.0 cm and forms a standing wave having two... Problem 18.26P: A string that is 30.0 cm long and has a mass per unit length of 9.00 103 kg/m is stretched to a... Problem 18.27P: In the arrangement shown in Figure P18.27, an object can be hung from a string (with linear mass... Problem 18.28P: In the arrangement shown in Figure P17.14, an object of mass m = 5.00 kg hangs from a cord around a... Problem 18.29P: Review. A sphere of mass M = 1.00 kg is supported by a string that passes over a pulley at the end... Problem 18.30P: Review. A sphere of mass M is supported by a string that passes over a pulley at the end of a... Problem 18.31P Problem 18.32P: Review. A solid copper object hangs at the bottom of a steel wire of negligible mass. The top end of... Problem 18.33P Problem 18.34P: The Bay of Fundy, Nova Scotia, has the highest tides in the world. Assume in midocean and at the... Problem 18.35P: An earthquake can produce a seiche in a lake in which the water sloshes back and forth from end to... Problem 18.36P: High-frequency sound can be used to produce standing-wave vibrations in a wine glass. A... Problem 18.37P Problem 18.38P Problem 18.39P: Calculate the length of a pipe that has a fundamental frequency of 240 Hz assuming the pipe is (a)... Problem 18.40P: The overall length of a piccolo is 32.0 cm. The resonating air column is open at both ends, (a) Find... Problem 18.41P: The fundamental frequency of an open organ pipe corresponds to middle C (261.6 Hz on the chromatic... Problem 18.42P Problem 18.43P: An air column in a glass tube is open at one end and closed at the other by a movable piston. The... Problem 18.44P Problem 18.45P Problem 18.46P: A shower stall has dimensions 86.0 cm 86.0 cm 210 cm. Assume the stall acts as a pipe closed at... Problem 18.47P Problem 18.48P Problem 18.49P: As shown in Figure P17.27, water is pumped into a tall, vertical cylinder at a volume flow rate R =... Problem 18.50P: As shown in Figure P17.27, water is pumped into a tall, vertical cylinder at a volume flow rate R.... Problem 18.51P: Two adjacent natural frequencies of an organ pipe are determined to be 550 Hz and 650 Hz. Calculate... Problem 18.52P: Why is the following situation impossible? A student is listening to the sounds from an air column... Problem 18.53P: A student uses an audio oscillator of adjustable frequency to measure the depth of a water well. The... Problem 18.54P: An aluminum rod is clamped one-fourth of the way along its length and set into longitudinal... Problem 18.55P Problem 18.56P Problem 18.57P: In certain ranges of a piano keyboard, more than one string is tuned to the same note to provide... Problem 18.58P Problem 18.59P: Review. A student holds a tuning fork oscillating at 256 Hz. He walks toward a wall at a constant... Problem 18.60P: An A-major chord consists of the notes called A, C#, and E. It can be played on a piano by... Problem 18.61P: Suppose a flutist plays a 523-Hz C note with first harmonic displacement amplitude A1 = 100 nm. From... Problem 18.62AP: A pipe open at both ends has a fundamental frequency of 300 Hz when the temperature is 0C. (a) What... Problem 18.63AP Problem 18.64AP: Two strings are vibrating at the same frequency of 150 Hz. After the tension in one of the strings... Problem 18.65AP Problem 18.66AP: A 2.00-m-long wire having a mass of 0.100 kg is fixed at both ends. The tension in the wire is... Problem 18.67AP: The fret closest to the bridge on a guitar is 21.4 cm from the bridge as shown in Figure P18.67.... Problem 18.68AP Problem 18.69AP: A quartz watch contains a crystal oscillator in the form of a block of quartz that vibrates by... Problem 18.70AP: Review. For the arrangement shown in Figure P17.40, the inclined plane and the small pulley are... Problem 18.71AP Problem 18.72AP: Two speakers are driven by the same oscillator of frequency f. They are located a distance d from... Problem 18.73AP: Review. Consider the apparatus shown in Figure 17.15 and described in Example 17.4. Suppose the... Problem 18.74AP: Review. The top end of a yo-yo string is held stationary. The yo-yo itself is much more massive than... Problem 18.75AP: On a marimba (Fig. P18.75), the wooden bar that sounds a tone when struck vibrates in a transverse... Problem 18.76AP: A nylon siring has mass 5.50 g and length L = 86.0 cm. The lower end is tied to the floor, and the... Problem 18.77AP: Two train whistles have identical frequencies of 180 Hz. When one train is at rest in the station... Problem 18.78AP: Review. A loudspeaker at the front of a room and an identical loudspeaker at the rear of the room... Problem 18.79AP Problem 18.80AP Problem 18.81AP Problem 18.82AP: A standing wave is set up in a string of variable length and tension by a vibrator of variable... Problem 18.83AP: Two waves are described by the wave functions y1(x,t)=5.00sin(2.00x10.0t)y2(x,t)=10.0cos(2.00x10.0t)... Problem 18.84AP Problem 18.85AP: Review. A 12.0-kg object hangs in equilibrium from a string with a total length of L = 5.00 m and a... Problem 18.86AP: Review. An object of mass m hangs in equilibrium from a string with a total length L and a linear... Problem 18.87CP: Review. Consider the apparatus shown in Figure P18.87a, where the hanging object has mass M and the... Problem 18.88CP Problem 18.9P: Two traveling sinusoidal waves are described by the wave functions y1 = 5.00 sin [(4.00x 1 200t)]...
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Concept explainers
The displacement of the air molecules in sound wave is modeled with the wave function s(x, t) = 5.00 nm cos (91.54 m−1 x − 3.14 × 104 s−1 t). (a) What is the wave speed of the sound wave? (b) What is the maximum speed of the air molecules as they oscillate in simple harmonic motion ? (c) What is the magnitude of the maximum acceleration of the air molecules as they oscillate in simple harmonic motion?
Definition Definition Special type of oscillation where the force of restoration is directly proportional to the displacement of the object from its mean or initial position. If an object is in motion such that the acceleration of the object is directly proportional to its displacement (which helps the moving object return to its resting position) then the object is said to undergo a simple harmonic motion. An object undergoing SHM always moves like a wave.
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