The problem is about comparing the frequencies of stationary sound waves formed in two pipes of the same length, but with different boundary conditions. Here's how we approach it:

1. First Pipe (Closed at one end, open at the other):

   • For a pipe closed at one end and open at the other, the fundamental frequency corresponds to a quarter-wavelength resonance ($\lambda/4$).
   • The lowest frequency (fundamental) is given as 4000 Hz.

2. Second Pipe (Open at both ends):

   • For a pipe open at both ends, the fundamental frequency corresponds to a half-wavelength resonance ($\lambda/2$).
   • The relationship between the frequency of the closed pipe and the open pipe can be derived by knowing that the fundamental frequency of an open-open pipe is half that of the fundamental frequency of a closed-open pipe (since an open-open pipe has twice the wavelength for the same length).

Thus, the fundamental frequency of the second pipe will be: $f_{\text{open-open}} = \frac{4000}{2} = 2000 \, \text{Hz}$

Answer: B) 2000 Hz

Would you like more details or have any questions? Here are some related questions to deepen your understanding:

1. How does the length of the pipe affect the frequency of the sound wave produced?
2. What is the relationship between wavelength and frequency for sound waves in air?
3. How do the harmonics differ between pipes open at both ends and pipes closed at one end?
4. How would the frequency change if the temperature of the air in the pipe increased?
5. Can the shape of the pipe affect the sound wave's behavior, or is it solely dependent on length?

Tip: For pipes closed at one end, only odd harmonics (e.g., 1st, 3rd, 5th) are allowed, while for pipes open at both ends, all harmonics (e.g., 1st, 2nd, 3rd) are possible.