What frequencies will a 1.85 m long tube produce in the audible range (20 Hz - 2

Question

What frequencies will a 1.85 m long tube produce in the audible range (20 Hz - 20,000 Hz) at 24.0°C for the following cases?

(a) the tube is closed at one end

lowest frequency 46.73 Correct: Your answer is correct. Hz

second lowest frequency 140.20 Correct: Your answer is correct. Hz

highest frequency (rounded to the nearest Hz) 19953 or 19954 Incorrect: Your answer is incorrect. Hz

(b) the tube is open at both ends lowest frequency 93.46 Correct: Your answer is correct. Hz

second lowest frequency 186.92 Correct: Your answer is correct. Hz

highest frequency (rounded to the nearest Hz) 19907 or 19906 Incorrect: Your answer is incorrect. Hz

I got the correct answer for f1 and f2 on both parts a and b. for some reason I cant find the correct answer for fmax on either. can someone please explain?

Explanation / Answer

Only certain combinations of wavelength and length of the pipe will result in a standing wave or resonance.

The conditions are given by:

For one end closed

? n = 4L / n for n=1,3,5,7, etc

?n = c / ? n = nc / 4L for n=1,3,5,7, etc

The frequencies ?n are called the resonant frequencies of the pipe.

Here only odd numbers are allowed

For n = 1, lowest frequency is c/ 4* 1.85 = 46.7 Hz

So at n = 427 , we will get maximum frequency = 19939 Hz

For both side open pipe

?n = c / ? n = nc / 2L for n=1,2,3,4, etc

Here all numbers are allowed

So for n= 1 frequency = 93.4 Hz

Maximum frequency will be at n = 214 is 19986 Hz

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