An air column that is open at both ends is 1.50m long. A specific frequency is heard resonating from the column what is the longest wavelength and it's associated frequency that could be responsible for this resonance? The speed of sound is 345m/s.
So what I did is:
v=2L
= 2*1.5
= 3
V = fx
245m/s = f*3
f = 115Hz
I'm not sure if this would be right though. /: thank you
Your answers are basically correct, but expressed using unconventional symbols.
λ usually represents the wavelength (v=velocity of sound in air).
So for the first harmonic, and
L=length of open tube of unknown diameter, then
λ=2L/1=2*1.5m=3m
Frequency, f (in Hz) is given by
f=nv/(2L) for the nth harmonic,
=1*345/(2*1.5)=115 Hz.
Okay, I see. Thank you!
Your calculation is almost correct, but there is a small mistake. The formula for the speed of sound in a tube open at both ends is given by v = 2Lf, where v is the speed of sound, L is the length of the tube, and f is the frequency.
In this case, the length of the tube is given as 1.50m and the speed of sound is given as 345m/s. Plugging these values into the formula, we have:
345m/s = 2 * 1.50m * f
Simplifying this equation, we have:
f = 345m/s / (2 * 1.50m)
f = 230Hz
So the resonant frequency associated with the longest wavelength in this air column is 230Hz. The longest wavelength can then be found using the formula for the wavelength of a wave: λ = v/f
λ = 345m/s / 230Hz
λ = 1.50m
Therefore, the longest wavelength associated with this resonance is 1.50m.
To find the longest wavelength and its associated frequency that can resonate in an open at both ends air column, we can use the formula:
λ = 2L/n
where:
λ is the wavelength
L is the length of the air column
n is the harmonic number
In this case, the harmonic number n will be the first harmonic (n = 1) since it is the fundamental frequency.
Given that the length of the air column L is 1.50m, and the speed of sound v is 345m/s, we can now calculate the wavelength:
λ = 2L/n
= 2(1.50)/1
= 3.00m
So the longest wavelength that could be responsible for this resonance is 3.00m.
Next, we can calculate the associated frequency using the formula:
v = fλ
where:
v is the speed of sound
f is the frequency
λ is the wavelength
Substituting the values:
345m/s = f * 3.00m
Rearranging the equation to solve for f:
f = 345m/s / 3.00m
= 115 Hz
Therefore, the longest wavelength associated with the resonance is 3.00m, and the frequency is 115 Hz.