f3 11 Hz (b) How many harmonic frequencies of this pipe lie in the audible range, from 20 Hz to 20000 Hz? 280 (c) What are the three lowest possible frequencies if the pipe is closed at on end and open at the other? f₁ = f3 = f5 = Hz Hz Hz

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Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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SOLUTION
(A) Find the frequencies if the pipe is open at both ends.
Substitute into whole harmonics
equation, with n = 1.
Multiply to find the second and third
harmonics.
This works out to n = 286.88, which
= 287
must be truncated down (n
gives a frequency over 2.00 x 104 Hz).
The next two harmonics are odd
multiples of the first:
V
2L
f₂ = 2f₁ = 139 Hz
f₁
LEARN MORE
(B) How many harmonics lie between 20 Hz and 20000 Hz for this pipe?
Set the frequency in the harmonics
equation equal to 2.00 x 104 Hz and
solve for n.
343 m/s
2. (2.46 m)
fn
=
=
f₁
V
(C) Find the frequencies for the pipe closed at one end.
Apply the one end open harmonics
equation with n = 1.
2L
n = 286
343 m/s
2(2.46 m)
=
= n
V
4L
f3 = 3f₁ = 105 Hz
343 m/s
4(2.46 m)
= 69.7 Hz
f3 = 3f₁ =
=
= 209 Hz
=
2.00 × 104 Hz
34.9 Hz
f5 = 5f₁ = 175 Hz
Transcribed Image Text:SOLUTION (A) Find the frequencies if the pipe is open at both ends. Substitute into whole harmonics equation, with n = 1. Multiply to find the second and third harmonics. This works out to n = 286.88, which = 287 must be truncated down (n gives a frequency over 2.00 x 104 Hz). The next two harmonics are odd multiples of the first: V 2L f₂ = 2f₁ = 139 Hz f₁ LEARN MORE (B) How many harmonics lie between 20 Hz and 20000 Hz for this pipe? Set the frequency in the harmonics equation equal to 2.00 x 104 Hz and solve for n. 343 m/s 2. (2.46 m) fn = = f₁ V (C) Find the frequencies for the pipe closed at one end. Apply the one end open harmonics equation with n = 1. 2L n = 286 343 m/s 2(2.46 m) = = n V 4L f3 = 3f₁ = 105 Hz 343 m/s 4(2.46 m) = 69.7 Hz f3 = 3f₁ = = = 209 Hz = 2.00 × 104 Hz 34.9 Hz f5 = 5f₁ = 175 Hz
f3
=
Hz
(b) How many harmonic frequencies of this pipe lie in the audible range, from 20 Hz to 20000 Hz?
280
(c) What are the three lowest possible frequencies if the pipe is closed at on end and open at the
other?
f₁ =
f3
f5 =
=
Hz
Hz
Hz
Transcribed Image Text:f3 = Hz (b) How many harmonic frequencies of this pipe lie in the audible range, from 20 Hz to 20000 Hz? 280 (c) What are the three lowest possible frequencies if the pipe is closed at on end and open at the other? f₁ = f3 f5 = = Hz Hz Hz
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