Textbook Question
A baby's mouth is 30 cm from her father's ear and 1.50 m from her mother's ear. What is the difference between the sound intensity levels heard by the father and by the mother?
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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 26a
The fundamental frequency of a pipe that is open at both ends is 524 Hz. How long is this pipe? If one end is now closed
Verified step by step guidance1
Understand that a pipe open at both ends supports standing waves with nodes at both ends. The fundamental frequency corresponds to the first harmonic, where the length of the pipe is half the wavelength of the sound wave.
Use the formula for the speed of sound in air, which is approximately 343 m/s at room temperature. The relationship between speed (v), frequency (f), and wavelength (λ) is given by: .
For the fundamental frequency, the wavelength is twice the length of the pipe. Therefore, the length of the pipe (L) can be expressed as: .
Substitute the given frequency (524 Hz) and the speed of sound (343 m/s) into the formula to find the length of the pipe: .
If one end of the pipe is closed, the pipe now supports a different set of harmonics. The fundamental frequency for a pipe closed at one end is a quarter wavelength. The new length of the pipe can be calculated using the same speed of sound and the new fundamental frequency, which would be half of the original frequency for the open pipe.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Fundamental Frequency
The fundamental frequency is the lowest frequency at which a system oscillates. For a pipe open at both ends, it is determined by the speed of sound in air and the length of the pipe. The fundamental frequency is the first harmonic, and it sets the basis for calculating higher harmonics.
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Open and Closed Pipes
An open pipe has both ends open, allowing air to move freely, creating antinodes at both ends. A closed pipe has one end closed, creating a node at the closed end and an antinode at the open end. This affects the harmonic series and the wavelengths of the standing waves that can form.
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Speed of Sound
The speed of sound in air is approximately 343 meters per second at room temperature. It is crucial for calculating the wavelength of sound waves in a pipe. The relationship between speed, frequency, and wavelength is given by the equation: speed = frequency × wavelength, which helps determine the pipe's length.
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Related Practice
Textbook Question
Standing sound waves are produced in a pipe that is 1.20 m long. For the fundamental and first two overtones, determine the locations along the pipe (measured from the left end) of the displacement nodes and the pressure nodes if (a) the pipe is open at both ends
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Textbook Question
Standing sound waves are produced in a pipe that is 1.20 m long. For the fundamental and first two overtones, determine the locations along the pipe (measured from the left end) of the displacement nodes and the pressure nodes if the pipe is closed at the left end and open at the right end.
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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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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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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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