To solve the question "All electromagnetic waves travel through a vacuum at:", we will analyze the properties of electromagnetic waves in a vacuum.
### Step-by-Step Solution:
1. **Understanding Electromagnetic Waves**:
Electromagnetic waves include a wide range of waves such as radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays. They all share the same fundamental characteristics when traveling through a vacuum.
2. **Speed of Electromagnetic Waves in Vacuum**:
In a vacuum, all electromagnetic waves travel at the same speed, which is denoted by the symbol \( c \). This speed is approximately \( 3 \times 10^8 \) meters per second.
3. **Medium Influence**:
The speed of electromagnetic waves can vary in different media (like air, water, glass, etc.), but in a vacuum, there are no particles or charges to impede their motion. Therefore, they travel at their maximum speed, \( c \).
4. **Analyzing the Options**:
- **Option 1**: The same speed - This is correct because all electromagnetic waves travel at speed \( c \) in a vacuum.
- **Option 2**: Speeds that are proportional to their frequency - This is incorrect; while the wavelength and frequency are related, the speed remains constant.
- **Option 3**: Speeds that are inversely proportional to their frequency - This is also incorrect for the same reason as above.
- **Option 4**: None of the above - This is incorrect since option 1 is correct.
5. **Conclusion**:
The correct answer is that all electromagnetic waves travel through a vacuum at the same speed, which is \( c = 3 \times 10^8 \) m/s.
### Final Answer:
All electromagnetic waves travel through a vacuum at the same speed, which is \( 3 \times 10^8 \) m/s.
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