Which of the following wavelengths will produce standing waves on a string that is 1.9 m long?
A.1.9
B.3.3
C.3.5
D.95
Obviously A will work
but note that 1.9/2 = .95
That would have a node at each end and would be the first resonance, lowest frequency. so also D
To determine which of the given wavelengths will produce standing waves on a string that is 1.9 m long, we need to use the equation for the fundamental frequency of a standing wave on a string:
f = v / λ
where:
- f is the frequency of the standing wave,
- v is the velocity of the wave, and
- λ is the wavelength of the wave.
In this case, we know the length of the string (L = 1.9 m), and since we're looking for the fundamental frequency, the wavelength of the wave will be twice the length of the string (λ = 2L). Thus:
f = v / (2L) ... (1)
Now, let's analyze the given options:
A. Wavelength = 1.9 m
B. Wavelength = 3.3 m
C. Wavelength = 3.5 m
D. Wavelength = 95 m
We can disregard option D because a wavelength of 95 m is significantly larger than the length of the string (1.9 m). This would not allow for any standing waves to form.
To determine the correct option among A, B, and C, we need to understand the relationship between the length of the string and the wavelength. For the fundamental frequency, the wavelength of the standing wave must be twice the length of the string (λ = 2L).
From the given options, option A with a wavelength of 1.9 m matches the length of the string. However, this signifies that only half a wave can fit on the string, and no complete standing wave can form. Therefore, option A is also incorrect.
Option B with a wavelength of 3.3 m and option C with a wavelength of 3.5 m are both longer than the length of the string (1.9 m). This means that both wavelengths can accommodate at least one complete wave on the string, allowing for the formation of a standing wave.
Thus, the correct answer is either option B or option C, depending on the specific situation and the values used for the velocity of the wave (v). Without further information, it is not possible to determine the exact correct wavelength.