Textbook Question
The fundamental frequency of a pipe that is open at both ends is 524 Hz. If one end is now closed, find the wavelength
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Ch 16: Sound & Hearing
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610
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Table of contents
- Ch 01: Units, Physical Quantities & Vectors41
- Ch 02: Motion Along a Straight Line67
- Ch 03: Motion in Two or Three Dimensions47
- Ch 04: Newton's Laws of Motion23
- Ch 05: Applying Newton's Laws59
- Ch 06: Work & Kinetic Energy14
- Ch 07: Potential Energy & Conservation8
- Ch 08: Momentum, Impulse, and Collisions18
- Ch 09: Rotation of Rigid Bodies42
- Ch 10: Dynamics of Rotational Motion48
- Ch 11: Equilibrium & Elasticity27
- Ch 12: Fluid Mechanics31
- Ch 13: Gravitation35
- Ch 14: Periodic Motion32
- Ch 15: Mechanical Waves25
- Ch 16: Sound & Hearing32
- Ch 17: Temperature and Heat36
- Ch 18: Thermal Properties of Matter38
- Ch 19: The First Law of Thermodynamics33
- Ch 20: The Second Law of Thermodynamics22
- Ch 21: Electric Charge and Electric Field36
- Ch 22: Gauss' Law24
- Ch 23: Electric Potential31
- Ch 24: Capacitance and Dielectrics18
- Ch 25: Current, Resistance, and EMF26
- Ch 26: Direct-Current Circuits30
- Ch 27: Magnetic Field and Magnetic Forces18
- Ch 28: Sources of Magnetic Field10
- Ch 29: Electromagnetic Induction28
- Ch 30: Inductance17
- Ch 31: Alternating Current21
- Ch 32: Electromagnetic Waves1
- Ch 33: The Nature and Propagation of Light20
- Ch 34: Geometric Optics34
- Ch 35: Interference19
- Ch 36: Diffraction25
- Ch 37: Special Relativity20
- Ch 38: Photons: Light Waves Behaving as Particles15
- Ch 39: Particles Behaving as Waves26
- Ch 40: Quantum Mechanics I: Wave Functions21
- Ch 41: Quantum Mechanics II: Atomic Structure25
- Ch 42: Molecules and Condensed Matter18
- Ch 43: Nuclear Physics16
- Ch 44: Particle Physics and Cosmology23
Young & Freedman Calc14th EditionUniversity PhysicsISBN: 9780321973610Not the one you use?Change textbook
Chapter 16, Problem 34b
Small speakers A and B are driven in phase at 725 Hz by the same audio oscillator. Both speakers start out 4.50 m from the listener, but speaker A is slowly moved away (Fig. E16.34)<IMAGE>. If A is moved even farther away than in part (a), at what distance d will the speakers next produce destructive interference at the listener’s location?
Verified step by step guidance1
Determine the wavelength of the sound wave using the formula: , where is the speed of sound (typically 343 m/s in air) and is the frequency (725 Hz).
For destructive interference, the path difference between the two speakers must equal an odd multiple of half the wavelength: , where is an integer (0, 1, 2, ...).
Calculate the initial path difference when both speakers are 4.50 m from the listener. Since they are equidistant, the initial path difference is 0 m.
To find the next occurrence of destructive interference, set the path difference to (the first odd multiple of half the wavelength). Solve for the distance that speaker A must be moved to create this path difference.
Add the calculated path difference to the original distance of speaker A (4.50 m) to determine the new distance of speaker A from the listener.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Destructive Interference
Destructive interference occurs when two waves meet in such a way that their crests and troughs align oppositely, resulting in a reduction or cancellation of the overall wave amplitude. This typically happens when the path difference between the two waves is an odd multiple of half the wavelength. Understanding this concept is crucial for determining the conditions under which the sound waves from speakers A and B will interfere destructively at the listener's location.
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Wavelength and Frequency
The wavelength of a sound wave is the distance between successive crests (or troughs) and is inversely related to its frequency, which is the number of cycles per second measured in Hertz (Hz). For a frequency of 725 Hz, the wavelength can be calculated using the speed of sound in air (approximately 343 m/s), allowing us to determine the specific distances at which interference occurs. This relationship is essential for solving the problem of finding the distance at which destructive interference happens.
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Path Difference
Path difference refers to the difference in distance traveled by two waves from their respective sources to a common point, such as the listener's location. For destructive interference to occur, this path difference must equal an odd multiple of half the wavelength. In this scenario, as speaker A is moved away, calculating the path difference between the sound waves from speakers A and B will help identify the specific distance at which the listener experiences destructive interference.
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Related Practice
Textbook Question
Small speakers A and B are driven in phase at 725 Hz by the same audio oscillator. Both speakers start out 4.50 m from the listener, but speaker A is slowly moved away (Fig. E16.34). At what distance d will the sound from the speakers first produce destructive interference at the listener's location?
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Textbook Question
Two small stereo speakers are driven in step by the same variable-frequency oscillator. Their sound is picked up by a microphone arranged as shown in Fig. E16.39. For what frequencies does their sound at the speakers produce constructive interference?
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Textbook Question
Two loudspeakers, A and B (Fig. E16.35), are driven by the same amplifier and emit sinusoidal waves in phase. Speaker B is 2.00 m to the right of speaker A. Consider point Q along the extension of the line connecting the speakers, 1.00 m to the right of speaker B. Both speakers emit sound waves that travel directly from the speaker to point Q. What is the lowest frequency for which constructive interference occurs at point Q?
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Textbook Question
Two loudspeakers, A and B (Fig. E16.35), are driven by the same amplifier and emit sinusoidal waves in phase. Speaker B is 2.00 m to the right of speaker A. Consider point Q along the extension of the line connecting the speakers, 1.00 m to the right of speaker B. Both speakers emit sound waves that travel directly from the speaker to point Q. What is the lowest frequency for which destructive interference occurs at point Q?
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Textbook Question
The fundamental frequency of a pipe that is open at both ends is 524 Hz. the frequency of the new fundamental.
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