MCAT Physics Question 97: Answer and Explanation
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Question: 97
7. What is the angular frequency of the third harmonic in a pipe of length 0.6 m with one closed end? (Note: The speed of the sound is approximately 
)
- A. 213 radians per second
- B. 425π radians per second
- C. 425 radians per second
- D. 850π radians per second
Correct Answer: D
Explanation:
The angular frequency is related to the frequency of a wave through the formula ω = 2πf. Thus, our initial task is to calculate the frequency of the wave. Knowing its speed, we determine the frequency by first calculating its wavelength (ν = fλ). For the third harmonic of a standing wave in a pipe with one closed end, the wavelength is
The frequency of the wave is therefore
Finally, obtain the angular frequency simply by multiplying the frequency of the wave by 2π:
ω = 2πf = 850π radians per second