A. A tube is open only at one end. A certain harmonic produced by the tube has a

Question

A. A tube is open only at one end. A certain harmonic produced by the tube has a frequency of 571 Hz. The next higher harmonic has a frequency of 799 Hz. The speed of sound in air is 343 m/s. (a) What is the integer n that describes the harmonic whose frequency is 571 Hz? (b) What is the length of the tube?

B. A person hums into the top of a well (tube open at only one end) and finds that standing waves are established at frequencies of 36.1, 60.2, and 84.2 Hz. The frequency of 36.1 Hz is not necessarily the fundamental frequency. The speed of sound is 343 m/s. How deep is the well?

Explanation / Answer

part A:

let fundamnetal freqeuncy is f.
nth harmonic has frequency 571 Hz and (n+1)th harmonic has frequency 799 Hz

as a tube with one end open produces only odd harmonics,
let
then (2*n+1)*f=571
(2*n+3)*f=799

subtracting the first equation from second equation,

2*f=799-571=228 Hz
==>f=114 Hz

so for 571 Hz, 2*n+1=571/114=5

hence 571 Hz is the 5th harmonic.

b)for fundamental frequency, length of the tube=wavelength/4

as we know, frequency*wavelength=speed of the wave

==>114*wavelength=343
==>wavelength=3.0087 m

hence length=3.0087/4=0.7521 m

Part B:

let fundamental frequency=f

then (2*n+1)*f=36.1 Hz
(2*n+3)*f=60.2 Hz
substracting first equation from second,

2*f=24.1 Hz
==>f=24.1/2=12.05 Hz

speed=343 m/s

wavelength=speed/frequency=28.464 m

then depth of the well=wavelength/4=7.116 m

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.