Question

1. A string of length 1.23 m vibrates in such a way that a standing wave with wavelength 0.820 m forms. What harmonic is the string vibrating at?

fourth harmonic

first harmonic

second harmonic

third harmonic

2. When a violin and guitar both play the same note, the two instruments still sound very distinct from one another. Which of the following attributes accounts for this difference?

power

amplitude

frequency

timbre

3.
A wave travels down a string with a velocity of 512 m/s. If the string has a length of 6.84 meters, what is the second harmonic frequency of this string?

74.9 Hz

165 Hz

3500 Hz

37.1 Hz

4. How long would a closed tube have to be in order to hear the 5th harmonic at 4000 Hz on an open tube? Assume the speed of sound is 340 m/s.

0.21 m

0.44 m

0.11 m

0.51 m

5. If a rope is held fixed on both ends, how many antinodes are there in the 3rd harmonic?

6

3

4

5

6. A certain open tube has a fundamental frequency of 410 Hz. What is the frequency of the third harmonic of this open tube?

771 Hz

1230 Hz

137 Hz

410 Hz

7.
A tuning fork is struck and placed over a cup of water. Describe the standing wave that is created.

The tuning fork is an antinode and the water is a node

Both are antinodes

The tuning fork is an antinode and the water is an antinode

Both are nodes

8.
Which situation will only allow odd harmonics?

Tube open at both ends

Tube open at one end

Tube open at the midpoint

9. The fundamental frequency of a certain 64.5 cm string is 352 Hz. Based on this information, what is the velocity of the wave traveling in this string?

119 m/s

343 m/s

454 m/s

227 m/s

10.
If you were to draw a 3rd harmonic of a tube open at both ends, what would you draw at the ends of the tube?

antinodes on both ends

antinode on one end and node the other end

nodes on both ends

Answer 1

Here are the answers to your questions:

1. **What harmonic is the string vibrating at?**
- Wavelength (λ) = 0.820 m
- Length of string (L) = 1.23 m
- Harmonics for a string fixed at both ends can be calculated using the formula:
\[ \text{Length} = n \times \frac{\lambda}{2} \]
where \( n \) is the harmonic number.

Rearranging gives:
\[ n = \frac{2L}{\lambda} = \frac{2 \times 1.23 \, \text{m}}{0.820 \, \text{m}} \approx 3 \]

- **Answer: Third harmonic**

2. **Which attribute accounts for the distinct sound of the violin and guitar?**
- **Answer: Timbre**

3. **What is the second harmonic frequency of this string?**
- Wave velocity (v) = 512 m/s
- Length of the string (L) = 6.84 m
- The frequency of the second harmonic is calculated by:
\[ f = \frac{n \cdot v}{2L} \]
Here \( n = 2 \) for the second harmonic:
\[ f = \frac{2 \cdot 512 \, \text{m/s}}{2 \cdot 6.84 \, \text{m}} \approx 74.9 \, \text{Hz} \]

- **Answer: 74.9 Hz**

4. **How long would a closed tube have to be for the 5th harmonic at 4000 Hz?**
- To find the length of a closed tube for the 5th harmonic, we use the formula:
- \( L = \frac{n \cdot v}{4f} \)
- For the 5th harmonic, \( n = 5 \) and \( v = 340 \, \text{m/s} \):
\[ L = \frac{5 \cdot 340 \, \text{m/s}}{4 \cdot 4000 \, \text{Hz}} = \frac{1700}{16000} = 0.10625 \, \text{m} \approx 0.11 \, \text{m} \]

- **Answer: 0.11 m**

5. **How many antinodes are there in the 3rd harmonic?**
- In the 3rd harmonic of a string fixed at both ends, the number of antinodes is equal to \( n \):
- **Answer: 3**

6. **What is the frequency of the third harmonic of this open tube?**
- The frequency of the nth harmonic in an open tube is given by \( f_n = n \cdot f_1 \).
- Here \( f_1 = 410 \, \text{Hz} \) and for the third harmonic \( n = 3 \):
\[ f_3 = 3 \cdot 410 \, \text{Hz} = 1230 \, \text{Hz} \]

- **Answer: 1230 Hz**

7. **Describe the standing wave created by the tuning fork over the cup of water.**
- The tuning fork creates a standing wave where the fork is an antinode (vibrating) and the water surface (stationary) will act as a node.
- **Answer: The tuning fork is an antinode and the water is a node**

8. **Which situation will only allow odd harmonics?**
- **Answer: Tube open at one end**

9. **What is the velocity of the wave traveling in this string?**
- The velocity can be calculated using the formula:
\[ v = f_1 \cdot \lambda_1 \]
- For the fundamental frequency:
\[ \lambda_1 = 2L = 2 \cdot 0.645 \, \text{m} = 1.290 \, \text{m} \]
\[ v = 352 \, \text{Hz} \cdot 1.290 \, \text{m} \approx 454 \, \text{m/s} \]

- **Answer: 454 m/s**

10. **If you were to draw a 3rd harmonic of a tube open at both ends, what would you draw at the ends of the tube?**
- For a tube open at both ends, both ends are antinodes.
- **Answer: Antinodes on both ends**