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.