Investigation 10
Waves and Sound
1. The two diagrams show waves on a string that are traveling toward each other. Draw what happens when the waves meet and what happens a short time after they meet.
a.
b.
c.
2. A source of sound (e.g., a siren, a speaker, a tuning fork, etc.) is emitting sound in all directions. The frequency of the sound is constant. Draw a diagram showing the wavefronts being emitted from the sound source. (Show at least five wavefronts.)
a. The source of sound is stationary. b. The source of sound is moving to the right.
c. What does the distance from one wavefront to the next wavefront represent?
d. When the source of sound is moving to the right, what happens to the
1) wavelength of the sound?
2) frequency of the sound?
3. A harmonic, longitudinal wave is sent along a slinky. The distance from a rarefaction to an adjacent compression is 0.5 meters. The waves are traveling along the slinky at a speed of 2 m/sec.
a. What is the value of the wavelength of the wave?
b. What is the value of the frequency of the wave?
4. Sound waves travel faster through steel than air. Explain why.
5. The fundamental frequency of a 1.2 meters long guitar string is 220 Hz. The shape of the oscillations on the string when it is oscillating in its fundamental frequency is shown.
a. What is the wavelength of the wave on the string?
b. How fast are the waves traveling on the string?
The string is plucked again and is then lightly touched at a point that is one-third the length of the string away from the end of the string producing three loops. (See diagram.)
c. How many nodes are there?
d. How many antinodes are there?
e. What is the name of this harmonic?
f. What is the name of this overtone?
g. What is the wavelength of the standing waves?
h. What is the frequency of oscillation of the string?
6. The air in a tube that is open at both ends is resonating in its fundamental frequency (first harmonic). The speed of sound is 345 m/s and the length of the tube is 0.20 m.
a. What is the wavelength of the wave in the tube?
b. Find the frequency at which the air in the tube is resonating.
c. If the air in the tube is resonating in its first overtone, then find that frequency.
7. Suppose the tube is open at one end and closed at the other, and is oscillating (or resonating) in its fundamental frequency (first harmonic) of 328 Hz. The distance from the open end of the tube to the closed end of the tube is 0.26 meters.
a. The closed end of the tube acts like a node of the oscillation. What is a node?
b. The open end of the tube acts like an antinode of the oscillation. What is an antinode?
c. Nodes and antinodes alternate in a standing wave. The diagram below shows alternating antinodes (A) and nodes (N). Starting with the antinode on the left, indicate how long one wavelength is. Also, starting with the node on the far right, indicate how long one wavelength is.
A N A N A N A N A N
d. What is the value of the wavelength of the sound wave that is resonating in the 0.26 meter long open-closed tube?
e. What is the value of the speed of sound in the air in the tube?