A 2.2 m-long string is fixed at both ends and tightened until the wave speed is 50 m/s. What is the frequency of the standing wave shown in the figure?
Answer in Hz.
I've been working on it for a while but cant figure out...
Without the figure, or a description of it, we can't help you. Use the figure to determine the wavelength. It will be twice the distance between two nodes (zeroes) of the standing wave pattern. Then use
(frequency) * (wavelength) = (wave speed) to get the frequency.
there are 6 nodes in the diagram
To find the frequency of the standing wave, we need to use the wave speed and the length of the string.
The formula to calculate the frequency of a standing wave is:
frequency (f) = wave speed (v) / wavelength (λ).
Since the string is fixed at both ends, the wavelength of the standing wave is twice the length of the string.
wavelength (λ) = 2 * length of the string.
Substituting this into the formula, we have:
frequency (f) = wave speed (v) / (2 * length of the string).
Given that the wave speed is 50 m/s and the length of the string is 2.2 m, we can calculate the frequency as follows:
f = 50 m/s / (2 * 2.2 m).
f ≈ 11.36 Hz.
Therefore, the frequency of the standing wave is approximately 11.36 Hz.
To find the frequency of the standing wave, we need to know the wavelength. The wavelength is the distance between corresponding points on the wave, which in this case is the distance between two consecutive nodes or antinodes.
Given that the length of the string is 2.2 m, and the standing wave is shown in the figure, we can assume that the length of the string represents one-half of a wavelength (half of a complete wave).
So, we can express the wavelength as:
λ = 2 * L
λ = 2 * 2.2 m
= 4.4 m
Now, we can use the formula to find the frequency (f) of a wave, which is:
v = f * λ
Where:
v = wave speed (given as 50 m/s)
f = frequency (unknown)
λ = wavelength (calculated as 4.4 m)
Rearranging the formula, we have:
f = v / λ
f = 50 m/s / 4.4 m
≈ 11.36 Hz
Therefore, the frequency of the standing wave shown in the figure is approximately 11.36 Hz.