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Question

The two nearest harmonics of a tube closed at one end and open at the other end are 220 Hz220 \text{ Hz} and 260 Hz260 \text{ Hz}. What is the fundamental frequency of the system?

A

10 Hz10 \text{ Hz}

B

20 Hz20 \text{ Hz}

C

30 Hz30 \text{ Hz}

D

40 Hz40 \text{ Hz}

Step-by-Step Solution

  1. Identify the Properties of the Tube: For a tube closed at one end and open at the other (closed organ pipe), only odd harmonics are present . The frequencies of these harmonics are given by fn=nf1f_n = n f_1, where n=1,3,5,n = 1, 3, 5, \dots and f1f_1 is the fundamental frequency.
  2. Set up the Equation: Let the two nearest (consecutive) harmonics be nf1n f_1 and (n+2)f1(n+2) f_1. Given: nf1=220 Hzn f_1 = 220 \text{ Hz} (n+2)f1=260 Hz(n+2) f_1 = 260 \text{ Hz}
  3. Calculate the Fundamental Frequency: Subtracting the first equation from the second gives the difference between consecutive harmonics: (n+2)f1nf1=260220(n+2) f_1 - n f_1 = 260 - 220 2f1=40    f1=20 Hz2 f_1 = 40 \implies f_1 = 20 \text{ Hz} Therefore, the fundamental frequency of the system is 20 Hz20 \text{ Hz}.

Exam Context & Concepts Covered

This question aligns with the NEET PHYSICS syllabus, specifically targeting concepts from WAVE. Mastering this topic is crucial for scoring well in the upcoming medical entrance examinations. Solving conceptually related problems will help you understand the nuances of these concepts and improve your problem-solving speed.

PHYSICSWAVEnearestharmonicsclosedfundamentalfrequency

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