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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
16장, 문제 40

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.

검증된 단계별 안내
1
Understand that an organ pipe open at one end and closed at the other supports a fundamental frequency where the length of the pipe is one-fourth of the wavelength. This is because the closed end is a node and the open end is an antinode.
Calculate the fundamental frequency of the original pipe using the formula: \( f_1 = \frac{v}{4L} \), where \( v \) is the speed of sound in air (approximately 343 m/s) and \( L \) is the length of the pipe (1.14 m).
Calculate the new length of the second pipe after it is lengthened by 2.00 cm. Convert this length to meters and use it to find the new fundamental frequency \( f_2 \) using the same formula: \( f_2 = \frac{v}{4(L + 0.02)} \).
Determine the beat frequency produced when the two pipes are played together. The beat frequency is the absolute difference between the two fundamental frequencies: \( f_{beat} = |f_1 - f_2| \).
Summarize the process: Calculate \( f_1 \) and \( f_2 \) using the given lengths and the speed of sound, then find the beat frequency by taking the absolute difference between these two frequencies.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.
영상 길이:
4m

주요 개념

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

Fundamental Frequency of a Pipe

The fundamental frequency of a pipe open at one end and closed at the other is determined by the length of the pipe and the speed of sound. The formula is f = v / (4L), where v is the speed of sound and L is the length of the pipe. This frequency represents the lowest frequency at which the pipe resonates.
추천 영상:
가이드 코스
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Circumference, Period, and Frequency in UCM

Beat Frequency

Beat frequency occurs when two sound waves of slightly different frequencies interfere with each other. The beat frequency is the absolute difference between the two frequencies, given by f_beat = |f1 - f2|. This results in a periodic variation in sound intensity, perceived as beats.
추천 영상:

Effect of Length Change on Frequency

Changing the length of a pipe affects its fundamental frequency. For a pipe open at one end, increasing the length decreases the frequency, as the wavelength of the sound wave increases. The new frequency can be calculated using the modified length in the fundamental frequency formula.
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