If you have three waves corresponding to to the lowest three frequencies of vibrations of a 30 cm air column, what is the wavelength of the standing wave in each case? What frequency is heard in each pipe?

The only information I have is that the speed of sound in air is 331 m/s

To find the wavelength and frequency of the standing wave in each case, we need to use the equation:

v = f * λ

where:
v = speed of sound in air (331 m/s)
f = frequency of the wave
λ = wavelength of the wave

In this case, we are given the lowest three frequencies of vibrations of a 30 cm air column. Let's consider each case one by one.

Case 1: Lowest Frequency
For the lowest frequency, we consider the fundamental frequency or the first harmonic. The first harmonic has one complete wave in the air column.

So, we know the frequency (f) is the lowest frequency, and the wavelength (λ) is the length of the column (30 cm = 0.3 m).

Using the equation v = f * λ and rearranging it to solve for f, we have:
f = v / λ
f = 331 m/s / 0.3 m
f ≈ 1103.33 Hz

Therefore, the frequency heard in this case is approximately 1103.33 Hz.

Case 2: Second Lowest Frequency
For the second lowest frequency, we consider the second harmonic. The second harmonic has two complete waves in the air column.

In this case, the wavelength (λ) is half the length of the column (0.3 m / 2 = 0.15 m).

Using the equation v = f * λ and rearranging it to solve for f, we have:
f = v / λ
f = 331 m/s / 0.15 m
f ≈ 2206.67 Hz

Therefore, the frequency heard in this case is approximately 2206.67 Hz.

Case 3: Third Lowest Frequency
For the third lowest frequency, we consider the third harmonic. The third harmonic has three complete waves in the air column.

In this case, the wavelength (λ) is one-third the length of the column (0.3 m / 3 = 0.1 m).

Using the equation v = f * λ and rearranging it to solve for f, we have:
f = v / λ
f = 331 m/s / 0.1 m
f = 3310 Hz

Therefore, the frequency heard in this case is 3310 Hz.

To summarize:
Case 1: Wavelength ≈ 0.3 m; Frequency ≈ 1103.33 Hz
Case 2: Wavelength ≈ 0.15 m; Frequency ≈ 2206.67 Hz
Case 3: Wavelength ≈ 0.1 m; Frequency = 3310 Hz