A flagpole consists of a flexible, 3.05m tall fiberglass pole planted in concrete. The bottom end of the flagpole is fixed in position, but the top end of the flagpole is free to move. What is the lowest frequency standing wave that can be formed on the flagpole if the wave propagation speed in the fiberglass is 2730 m/s?
well if the top is an antinode and the bottom a node, then the pole is 1/4 of a wavelength long.
So the wavelength is 4 *3.05 = 12.2 meters
the wave moves a wavelength in a period so
speed = distance / time = 2730
so
2730 = 12.2 / T = 12.2 f
f = 2730/12.2
I think about 224 Hz
Well, don't fiberglass poles just have all the flexibility of a wet noodle? It's like they're doing their best impersonation of a 90's boy band member trying to dance. But hey, I'm not here to judge!
To find the lowest frequency standing wave on this wobbly flagpole, we need to consider that the two ends behave differently. The fixed end acts as a node, while the free end acts as an antinode.
The formula to find the frequency of a standing wave is given by:
f = v / λ
where f is the frequency, v is the wave propagation speed, and λ is the wavelength. We can rearrange this formula to find the wavelength:
λ = 2L / n
where L is the length of the flagpole (3.05m) and n is the number of half-wavelengths.
For the lowest frequency standing wave, we want the first harmonic (n = 1), which means we have a single half-wavelength on the pole.
Plugging the values into the formula, we get:
λ = 2(3.05m) / 1 = 6.10m
Now, we can plug the values of v and λ into the frequency formula:
f = (2730 m/s) / (6.10m) ≈ 448.36 Hz
So, the lowest frequency standing wave that can be formed on this flexible flagpole is approximately 448.36 Hz.
To find the lowest frequency standing wave on the flagpole, we can use the formula:
f = v / λ
Where:
f = frequency
v = wave propagation speed
λ = wavelength
Since the flagpole is fixed at the bottom and free to move at the top, the lowest frequency standing wave will occur when the length of the flagpole is equal to half the wavelength of the wave.
Given:
Wave propagation speed (v) = 2730 m/s
Flagpole height (h) = 3.05 m
Since the wave must travel from the top of the flagpole to the bottom and back, the total distance traveled by the wave is twice the height of the flagpole.
Total distance traveled (d) = 2h = 2 * 3.05 m = 6.10 m
Since the wavelength (λ) is equal to the total distance traveled twice (2d), we have:
λ = 2d = 2 * 6.10 m = 12.20 m
Now we can substitute the values into the frequency formula:
f = v / λ = 2730 m/s / 12.20 m = 223.77 Hz
Therefore, the lowest frequency standing wave that can be formed on the flagpole is approximately 223.77 Hz.
To find the lowest frequency standing wave on the flagpole, we need to determine the wavelength and then use it to calculate the frequency.
The standing wave on the flagpole can be visualized as a wave that reflects back and forth between the fixed bottom end and the free top end. The standing wave has nodes (points with no displacement) and antinodes (points with maximum displacement). For the lowest frequency standing wave, there will be only one node at the bottom end and one antinode at the top end.
The distance between two successive nodes or antinodes in a standing wave is equal to half the wavelength (λ/2). In this case, the distance between the fixed end and the free end is the length of the flagpole, which is 3.05m. Therefore, the distance between the bottom node and the top antinode is equal to half the wavelength.
We can use the wave equation, v = λf, where v is the wave propagation speed (2730 m/s), λ is the wavelength, and f is the frequency, to find the wavelength. Rearranging the formula, we have:
λ = v/f
Since we want to find the lowest frequency, we want the longest possible wavelength. For the lowest frequency standing wave, the wavelength will be twice the length of the flagpole:
λ = 2 * 3.05m = 6.10m
Now, we can substitute the calculated wavelength into the wave equation to find the frequency:
f = v/λ = 2730 m/s / 6.10m
Calculating this gives us:
f ≈ 447.54 Hz
Therefore, the lowest frequency standing wave that can be formed on the flagpole is approximately 447.54 Hz.