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Ch 16: Sound & Hearing
Young & Freedman Calc - University Physics 15th Edition
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552당신이 사용하는 게 아니라요?교과서 변경
모든 교과서Young & Freedman Calc 15th EditionCh 16: Sound & Hearing문제 33b
16장, 문제 33b

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?
Diagram of two speakers A and B connected to an amplifier, with distances labeled for wave interference.

검증된 단계별 안내
1
Identify the path difference between the sound waves from speakers A and B to point Q. The distance from A to Q is 3.00 m (2.00 m + 1.00 m), and the distance from B to Q is 1.00 m.
Calculate the path difference: ΔL = L_AQ - L_BQ = 3.00 m - 1.00 m = 2.00 m.
For destructive interference, the path difference should be an odd multiple of half wavelengths: ΔL = (m + 0.5)λ, where m is an integer.
Express the wavelength in terms of frequency: λ = v/f, where v is the speed of sound in air (approximately 343 m/s).
Set up the equation for the lowest frequency (m = 0): 2.00 m = (0.5) * (343 m/s) / f. Solve for f to find the lowest frequency for destructive interference.

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이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
6m
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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Destructive Interference

Destructive interference occurs when two waves meet in such a way that their crests and troughs align oppositely, leading to a reduction in amplitude. For sound waves, this typically happens when the path difference between the waves from two sources is an odd multiple of half the wavelength. In this scenario, understanding how the distance between the speakers and the point of observation affects the phase relationship of the waves is crucial.
추천 영상:
가이드 코스
03:47
Wave Interference & Superposition

Path Difference

Path difference refers to the difference in distance traveled by two waves from their sources to a common point. In the context of the speakers A and B, the path difference to point Q is essential for determining whether constructive or destructive interference occurs. For destructive interference, the path difference must equal (n + 0.5)λ, where n is an integer and λ is the wavelength of the sound.
추천 영상:
가이드 코스
08:20
Mean Free Path

Frequency and Wavelength Relationship

The frequency of a wave is inversely related to its wavelength, described by the equation v = fλ, where v is the speed of sound, f is the frequency, and λ is the wavelength. In this problem, finding the lowest frequency that results in destructive interference at point Q requires calculating the corresponding wavelength based on the path difference. This relationship is fundamental in understanding how sound waves interact in this scenario.
추천 영상:
가이드 코스
05:08
Circumference, Period, and Frequency in UCM
관련 실천
교과서 질문

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?

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교과서 질문

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?

<Image>

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교과서 질문

A railroad train is traveling at 30.0 m/s in still air. The frequency of the note emitted by the train whistle is 352 Hz. What frequency is heard by a passenger on a train moving in the opposite direction to the first at 18.0 m/s and approaching the first?

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교과서 질문

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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교과서 질문

Two organ pipes, open at one end but closed at the other, are each 1.14 m long. One is now lengthened by 2.00 cm. Find the beat frequency that they produce when playing together in their fundamentals.

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교과서 질문

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?

3062
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