The fourth harmonic of 800 kHz is:
A. 200 kHz.
B. 400 kHz.
C. 3.20 MHz.
D. 4.00 MHz.
The Correct Answer and Explanation is:
The correct answer is:
D. 4.00 MHz
Explanation:
To understand this question, we first need to clarify what a harmonic frequency is.
Harmonics are integer multiples of a fundamental frequency. If you have a fundamental frequency ff, then:
- The 1st harmonic is 1×f=f1 \times f = f
- The 2nd harmonic is 2×f2 \times f
- The 3rd harmonic is 3×f3 \times f
- The 4th harmonic is 4×f4 \times f, and so forth.
Step-by-step solution:
- Given fundamental frequency:
f=800 kHzf = 800 \text{ kHz} - Find the 4th harmonic:
The 4th harmonic = 4×f=4×800 kHz4 \times f = 4 \times 800 \text{ kHz} - Calculate:
4×800 kHz=3200 kHz4 \times 800 \text{ kHz} = 3200 \text{ kHz} - Convert kHz to MHz:
Since 1000 kHz=1 MHz1000 \text{ kHz} = 1 \text{ MHz},
3200 kHz=3.2 MHz3200 \text{ kHz} = 3.2 \text{ MHz}
Why then is the correct answer 4.00 MHz (option D), not 3.20 MHz (option C)?
Let’s carefully reconsider the question and options:
- The 4th harmonic of 800 kHz means multiplying 800 kHz by 4, which is indeed 3200 kHz or 3.20 MHz.
- Option C is 3.20 MHz, which mathematically matches the 4th harmonic exactly.
This suggests the correct answer should be C. 3.20 MHz.
So the final correct answer is:
C. 3.20 MHz
Summary and Additional Explanation:
The concept of harmonics is critical in many fields like electronics, acoustics, and radio frequency engineering. The fundamental frequency is the base frequency of a waveform or oscillation. Harmonics are higher frequencies that occur at multiples of this fundamental frequency. They are important because they influence signal quality, bandwidth, and can cause distortion or resonance effects.
In this question, the fundamental frequency is 800 kHz, so each harmonic frequency is an integer multiple of 800 kHz:
- 1st harmonic = 800 kHz
- 2nd harmonic = 1600 kHz (1.6 MHz)
- 3rd harmonic = 2400 kHz (2.4 MHz)
- 4th harmonic = 3200 kHz (3.2 MHz)
Therefore, option C (3.20 MHz) is the mathematically accurate answer.
If you want a quick rule: To find the nth harmonic of a frequency, multiply the frequency by n, then convert the units accordingly.
Recap:
- Fundamental frequency: 800 kHz
- 4th harmonic = 4×800kHz=3200kHz=3.2MHz4 \times 800\text{kHz} = 3200\text{kHz} = 3.2\text{MHz}
- Correct answer: C. 3.20 MHz
If you want me to clarify why option D (4.00 MHz) might be considered, or if the question had a different fundamental frequency, just ask!