What's the shortest air column , closed at one end, that will resonate at a frequency of 440.0Hz when the speed of sound is 352 m/s

λ =v/f =352/440 = 0.8 m

L= λ/4=0.8/4 = 0.2 m

Could you please explain how you got that!

The answer should be 20.0cm and I just don't understand

The answer is in meters, just switch it to cm,

Why did the air column bring a measuring tape to the concert?

Because it wanted to find its perfect pitch at 440.0Hz!

As for your question, the shortest air column that will resonate at a frequency of 440.0Hz can be determined using the formula:

L = (v/2f)

Where:
L is the length of the air column
v is the speed of sound (352 m/s)
f is the frequency (440.0Hz)

Plugging in the values:

L = (352 m/s) / (2 * 440.0Hz)
L = 0.4 meters

So, the shortest air column, closed at one end, that will resonate at a frequency of 440.0Hz is 0.4 meters long. Make sure to measure twice and laugh once!

To determine the length of the air column that will resonate at a frequency of 440.0 Hz, we can use the formula:

λ = 2L/n

where:
- λ is the wavelength of the sound wave
- L is the length of the air column
- n is the harmonic number (for a closed tube, n can only be odd numbers)

From the formula, we can see that the resonant frequency is inversely proportional to the wavelength.

First, let's find the wavelength using the formula:

v = λf

where:
- v is the speed of sound
- λ is the wavelength
- f is the frequency

Rearranging the formula, we have:

λ = v/f

Substituting the given values, we get:

λ = 352 m/s / 440.0 Hz

Calculating this, we find:

λ = 0.8 m

Now, we can determine the length of the air column:

λ = 2L/n

Substituting the known values, we have:

0.8 m = 2L/1

Simplifying the equation, we find:

L = 0.4 m

Therefore, the shortest air column, closed at one end, that will resonate at a frequency of 440.0 Hz when the speed of sound is 352 m/s is 0.4 meters in length.