1. antinodes (max. vibration)
Longitudinal Standing Waves
nodes (no vibration)
antinodes (max. vibration)

2. STRING INSTRUMENTS
The sounds produced by vibrating strings are not very loud. Many stringed instruments make use of a sounding board or box, sometimes called a resonator, to amplify the sounds produced. The strings on a piano are attached to a sounding board while for guitar strings a sound box is used. When the string is plucked and begins to vibrate, the sounding board or box begins to vibrate as well. Since the board or box has a greater area in contact with the air, it tends to amplify the sounds.
On a guitar or a violin, the length of the
strings are the same, but their mass per
length is different. That changes the
velocity and so the frequency changes.

3. Wind instruments create sound through standing waves in a column of air.

5. vibrating air molecules
When air is blown over a bottle, it creates a standing longitudinal (sound) wave
Remember, this is a longitudinal wave even though we draw it like this to visualize the shape.
open end: antinode
vibrating air molecules
closed end: node

6. Air pressure Nodes verse air displacement Nodes…
This is complex but worth understanding!

8. Displacement and pressure variation are complementary pictures
Displacement and pressure variation are complementary pictures.  When particles are free to move you have a displacement anti-node, like the open end of a tube, and the variation in pressure is zero, hence a pressure node.  When particles are constrained by a wall you have a displacement node and the pressure variation at that wall is maximized hence a pressure anti-node.
At the right side where the tube end is closed, you can see that particles don't move through the end (there's a wall there). So, all of the particles that hit bounce back elastically (ideally) experiencing maximum change in velocity and therefore, causing maximum pressure while they are bouncing. After they've bounced there's a momentary lull in bounces and you get a minimum of pressure. So, the fact that the particles CANNOT move through the closed end (a displacement node) means you must get a pressure maximum variation (antinode). It's less obvious or intuitive (to me at least) other than by analogy that where there's an opening there is a displacement antinode (maximum in and out) there has to be a pressure node (no change).
Web based Physics teacher comments…

10. You can also ring a tuning fork over a bottle or tube, and if it creates wavelengths of just the right length, you’ll get a standing wave (loud sound).

11. ? How is a sound wave reflected back in an open end pipe?
Consider a low pressure region travelling along the tube towards the open end. The air outside is at atmospheric pressure, so when the low pressure region hits the end of the tube air from the atmosphere rushes in and creates a compression wave heading back down the tube. The opposite happens when a high pressure region hits the end of the tube.

12. CLOSED PIPE
Just like we did for strings, we can also derive a formula to calculate……
n = 1,3,5,…
The Harmonic Frequencies for a tube open at one end
speed of sound
odd harmonics only

13. Flute
Starting with all the valves closed, what happens to the pitch as I open the valves in order? Why?
Pitch increases b/c the length is increasing
Pitch increases b/c the length is decreasing
Pitch decreases b/c the length is increasing
Pitch decreases b/c the length is decreasing
Pitch increases b/c the harmonics are increasing

14. Trombone
What would have to happen to play a lower note on a trombone without changing the number of harmonics?
Increase the length
Decrease the length
Increase the length & blow faster
Increase the length & blow slower
Decrease the length & blow slower

15. A closed pipe has a fundamental frequency of 150 Hz
A closed pipe has a fundamental frequency of 150 Hz. Which of the following cannot be heard on this pipe?
A) 300 Hz
B) 450 Hz
C) 750 Hz
D) 1050 Hz
E) all of the above are possible.

19. Standing waves can also occur in a tube that is open at both ends
OPEN PIPE
Standing waves can also occur in a tube that is open at both ends

20. Harmonic Frequencies for a tube open at both ends
OPEN PIPE
A tube open at both ends has displacement antinodes, at the ends.
Harmonic Frequencies for a tube open at both ends
n = 1,2,3,4,…

21. An open pipe has a fundamental frequency of 140 Hz
An open pipe has a fundamental frequency of 140 Hz. Which of the following is NOT a harmonic which can be played on this pipe?
A) 280 Hz
B) 420 Hz
C) 560 Hz
D) 70 Hz
E) 1400 Hz

22. Hard!

23. Saxophone is closed so: L= 1/4 λ
A saxophone plays a tune in the key of B-flat. The saxophone has a third harmonic frequency of Hz when the speed of sound in air is 331 m/s. What is the length of the pipe that makes up the saxophone?
f' = f3/n
= 466.2/3
= Hz
Saxophone is closed so: L= 1/4 λ
n = 3
f3 = Hz
v = 331 m/s
= 0.53 m

24. An organ pipe that is open at both ends has a fundamental frequency of Hz when the speed of sound in air is 331 m/s. What is the length of this pipe?
f' = 370 Hz
v = 331 m/s
L= 1/2 λ
= m

25. What is the fundamental frequency of a viola string that is 35
What is the fundamental frequency of a viola string that is cm long when the speed of waves on this string is 346 m/s?
L = m
v = 346 m/s
L= 1/2 λ and λ = 2L
= Hz

26. L= 1/2 λ and λ = 2L v = λ f =2 L f = 2(1.32)(125) = 330 m/s
A pipe that is open at both ends has a fundamental frequency of 125 Hz. If the pipe is 1.32 m long, what is the speed of the waves in the pipe?
L= 1/2 λ and λ = 2L
v = λ f
=2 L f
= 2(1.32)(125)
= 330 m/s
f' = 125 Hz
L = 1.32 m

27. A pipe that is closed on one end has a seventh harmonic frequency of Hz. If the pipe is 1.53 m long, what is the speed of the waves in the pipe?
n = 7
f7 = Hz
L = 1.53 m
L= 7/4 λ and λ = 4/7 L
= m/s

28. Open-End vs Closed-End Tube
If both an open-ended instrument and a closed-end instrument are playing the same note at the same harmonic, which instrument has a longer tube?
Open-end
Closed-end
The same
Can’t be determined