An open organ pipe of length 0.744411 m and a closed one of length 1.10545 m are sounded together. What beat frequency is generated by the first overtone of the closed pipe with the fundamental of the open pipe? The speed of sound is 340 m/s.

Answer in units of Hz

To find the beat frequency generated by the first overtone of the closed pipe with the fundamental frequency of the open pipe, we need to first calculate the frequencies of both pipes.

For an open organ pipe, the fundamental frequency can be found using the formula:

f1 = v / (2L1)

where f1 is the fundamental frequency, v is the speed of sound, and L1 is the length of the open pipe.

Substituting the given values, we have:

f1 = 340 / (2 * 0.744411)

f1 ≈ 229.996 Hz

For a closed organ pipe, the fundamental frequency can be found using the formula:

f2 = v / (4L2)

where f2 is the fundamental frequency, v is the speed of sound, and L2 is the length of the closed pipe.

Substituting the given values, we have:

f2 = 340 / (4 * 1.10545)

f2 ≈ 77.042 Hz

The first overtone of the closed pipe is twice the fundamental frequency, so we have:

f3 = 2 * f2 ≈ 2 * 77.042 ≈ 154.084 Hz

Now, to find the beat frequency, we subtract the frequency of the open pipe from the frequency of the first overtone of the closed pipe:

Beat frequency = f3 - f1
= 154.084 - 229.996
≈ -75.912 Hz

Since beat frequency is the difference between two frequencies, it can be negative or positive. However, in this case, since the first overtone of the closed pipe has a lower frequency than the fundamental frequency of the open pipe, the beat frequency is negative.

Thus, the beat frequency is approximately -75.912 Hz.