if the shortest lenggth of the tube for resonance is 0.1m and next resonance length is 0.35m what is the frequency of the vibration
f=v/l
f=v/l2-l1
f=340/0.36-0.1
f=340/0.26
f=1384.62Hz
To find the frequency of vibration, we can use the formula for the length of a resonant tube:
L₁ = (n * λ) / 4
where L₁ is the shortest length, n is the harmonic number, and λ is the wavelength.
From the given information, we know that the shortest length (L₁) is 0.1m and the next resonance length is 0.35m.
Let's find the harmonic number (n) for the next resonance length:
L₂ = (n * λ) / 4
0.35m = (n * λ) / 4
We can rearrange this equation to solve for λ:
λ = (4 * L₂) / n
To find n, we need to compare the two resonance lengths:
L₁ = (n * λ) / 4
0.1m = (n * λ) / 4
Now, we can solve for λ in terms of n using this equation:
λ = (4 * L₁) / n
Since both expressions for λ are equal, we can set them equal to each other:
(4 * L₂) / n = (4 * L₁) / n
Simplifying, we have:
4 * L₂ = 4 * L₁
Dividing by 4 on both sides:
L₂ = L₁
Since the two resonance lengths are equal, it means that the harmonic number is 2.
Now let's go back to the equation for wavelength:
λ = (4 * L₁) / n
λ = (4 * 0.1m) / 2
λ = 0.2m
Finally, we can find the frequency using the formula:
f = v / λ
Where v is the speed of sound. Let's assume v is approximately 343 m/s (the speed of sound in dry air at 20°C).
f = 343 m/s / 0.2m
f ≈ 1715 Hz
Therefore, the frequency of the vibration is approximately 1715 Hz.
To determine the frequency of vibration for the given scenario, we need to make use of the formula for the fundamental frequency of a closed tube:
f = v / λ
Where:
- f indicates the frequency,
- v represents the speed of sound, and
- λ denotes the wavelength.
Given that the shortest length of the tube for resonance is 0.1 m and the next resonance length is 0.35 m, we can find the wavelength as follows:
λ = L₁ - L₂
Where:
- L₁ is the shortest length, and
- L₂ is the next resonance length.
Substituting the given values:
λ = 0.35 m - 0.1 m
= 0.25 m
Now, we need to determine the speed of sound to calculate the frequency. In air, the speed of sound is approximately 343 m/s at room temperature.
Substituting the values into the formula:
f = 343 m/s / 0.25 m
= 1372 Hz
Therefore, the frequency of vibration for this scenario is approximately 1372 Hz.