1. v = f fn = nf1  = 5558 m 343 = 5558(f) f = 0.0617 Hz 325th harmonic
Given:
L = 2779 m
n = 1 (fundamental frequency)
v = 343 m/s 1)
(open air column) a)
v = f
 = 5558 m
343 = 5558(f)
f = Hz b)
fn = nf1
325th harmonic
20 = n(0.0167)

2. v = f v = f  = 0.96 m 343 = 0.96(f) f = 357.3 Hz = 476.4 Hz
Given:
L = 48 cm = 0.48 m
n = 1 (fundamental frequency)
v = 343 m/s 2)
(open air column)
v = f
 = 0.96 m
343 = 0.96(f)
f = Hz
= Hz
L = 0.36 m
v = f
12 cm from the end
343 = (476.4)
 = 0.72 m

3. v = f open pipe f2 = 306.2 Hz; f3 = 459.3 Hz; f4 = 612.4 Hz3)
Given:
L = 112 cm = 1.12m
n = 1 (fundamental frequency)
v = 343 m/s
open pipe
f2 = Hz; f3 = Hz; f4 = Hz
(open air column)
closed pipe
f3 = Hz; f5 = Hz; f7 = Hz
open = 2.24 m
(closed air column)
closed = 4.48 m
v = f
open pipe
f1 = Hz
343 = 2.24(f)
closed pipe
f1 = 76.6 Hz
343 = 4.48(f)
fn = nf1
open pipe next three harmonics = 2, 3, 4
closed pipe next three harmonics = 3, 5, 7

4. 60 Hz 100 Hz 140 Hz. f3 f5 f7 20 Hz These differ by how much ? 40 Hz4)
(closed air column)
These differ by how much ?
40 Hz
60 Hz Hz Hz. f3 f5 f7
These differ by how much ?
40 Hz
By how much less would you expect the
harmonic before 60 Hz to be?
40 Hz
What is the frequency of the harmonic before 60 Hz?
I know this is the fundamental frequency since 40 Hz below this would be negative
20 Hz

5. closed air column 88 Hz 264 Hz 440 Hz 616 Hz. f3 f5 f7 88 Hz5)
88 Hz
These differ by how much ?
176 Hz
264 Hz Hz Hz. f3 f5 f7
These differ by how much ?
176 Hz
By how much less would you expect the
harmonic before 264 Hz to be?
176 Hz
What is the frequency of the harmonic before 264 Hz?
I know this is the fundamental frequency since 176 Hz below this would be negative
88 Hz

6. v = f v = f 343 = (262)  = 1.309 m 337 = 1.309(f) L = 65.5 cm
Given:
f = 262 Hz
n = 1 (fundamental frequency)
v = 343 m/s 6)
(open air column)
v = f
343 = (262)
 = m
v = f
337 = 1.309(f)
L = 65.5 cm
f = Hz

7. v = f 343 = (294)  = 1.16 m L = 0.58 m 7.5 cm from the end Given:
f = 294 Hz
n = 1 (fundamental frequency)
v = 343 m/s 7)
(open air column)
v = f
343 = (294)
 = 1.16 m
L = 0.58 m
7.5 cm from the end