Three successive resonance frequencies in an organ pipe are 3750Hz, 4250 Hz, and
ID: 1729831 • Letter: T
Question
Three successive resonance frequencies in an organ pipe are 3750Hz, 4250 Hz, and 4750 Hz. Is the pipe closed at one end or open atboth ends, and why?1. There are no even harmonics, so the pipe must be fixed at oneend only.
2. There are no odd harmonics, so the pipe must be fixed at one endonly.
3. There are both odd and even harmonics, so the pipe must be fixedat one end only.
4. There are no odd harmonics, so the pipe must be fixed at bothone end.
5. There are no even harmonics, so the pipe must be fixed at bothend.
6. There are both odd and even harmonics, so the pipe must be fixedat both end.
What is the fundamental frequency? The speed of sound is 340 m/s.Answer in units of Hz.
What is the length of the pipe? Answer in units of cm.
Explanation / Answer
Successive frequencies -3750 Hz, 4250 Hz and 4750 Hz Highest commonfactor = 250 Hz Ratio offrequencies = ( 3750 / 250 ) : (4250 / 250 ) : ( 4750 / 250 ) = 15 : 17 : 19 Thereare no even harmonics. Hence, it is a pipe closed at oneend. ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ Fundamental frequency, f = 250Hz ( It is equal to HCF of thefrequencies ) Speedof sound, V = 340 m/s Fundamentalfrequency, f = ( V / 4 L ) Length of thepipe, L = ( V / 4 f ) = 340 / 1000 = 0.34 m = 34 cm
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