Resonance Practice problems
Name: ________________
1. Draw the 3rd harmonic of a standing wave produced in
a) String
b) Open pipe
c) Closed pipe
2. The human frequency range is _______________ to __________________.
String and Open Tubed Instruments
1. If the fundamental frequency is 20Hz, then the 2nd harmonic
a) on a string is _________Hz
b) In an open pipe is _________ Hz
2. Given that a bugle (an open tube) produces fundamental frequency of 50Hz, find the
a. 1st Harmonic ___________________
b. 2nd Harmonic ___________________
3. A note on a piano has a pitch of 55 Hz. What is the pitch of the note that is one octave (the next
harmonic) higher
4. A note played on a guitar has a pitch of 32 Hz. What is the pitch of a note that is 4 octaves
higher?
5. If you shorten the string on a guitar to 0.2 m. Assume the speed to be 343 m/s. What is the
pitch of the note?
6. A guitar string with a length of .8m is plucked. The speed of a wave on the string is 400 m/s.
Calculate the fundamental frequency of the string.
7. On a cold February day, the air temperature is 8° C. A wind chime that’s open on both ends is
blowing in the wind and creates a 560 Hz note. What is the length of the wind chime?
8. If there is an open pipe and the length between two consecutive resonance (or resonant sound)
is 2 m. Find the frequency of the tuning fork producing the standing waves. Use the speed of
sound as 343m/s.
Closed Tube Instruments
9.
If there is a closed pipe and the first harmonic or the fundamental resonant sound is heard at
.10 m length, find the frequency of the tuning fork. Use the speed of sound as 343m/s.
10. If the spacing between 2 resonant points in a closed tube is .50m. Find the frequency of tuning
fork being used? Use the speed of sound as 343m/s.
11. You play a 300 Hz note in a tube that is closed at one end. What is the pitch if you open the tube
at both ends?
12. Tommy and the Test Tubes are playing in a battle of the bands this weekend. The lead
instrumentalist uses a test tube with a 17.2 cm air column. The temperature of the air is 15°C.
Find the fundamental frequency of the tubes.
13. Joe the whistle maker knows the maximum volume for a whistle will occur if the length of the
whistle is exactly ¼ of the wavelength. If Joe wants to make a whistle that plays at a pitch of
320 Hz, how long must he make the whistle?
Musical Notes
14. Using the velocity of sound (at room temperature, 20°C) and given the pitch of notes on a piano,
calculate the wavelengths of the notes. v = ______m/s
Note
Pitch (Hz)
C
261.6
D
293.6
E
329.6
F
349.2
G
392
A
440
B
493.9
C
523.2
Wavelength