If a standing wave with 10 antinodes occurs at a frequency of 44.1 Hz, at what frequency would you look for the n = 2 standing wave?
To find the frequency at which the n = 2 standing wave occurs, we need to understand the relationship between the frequency and the number of antinodes in standing waves.
In a standing wave, the number of antinodes is related to the wavelength of the wave. The antinodes, also called nodes of displacement, are the points in a standing wave where the amplitude of the wave is at its maximum. The distance between two consecutive antinodes is equal to half of the wavelength.
In a standing wave, the frequency (f) is related to the wave speed (v) and wavelength (λ) through the formula:
f = v / λ
Since we are given the frequency (f = 44.1 Hz) for the n = 1 standing wave, we can find the wavelength (λ) using the formula:
λ = v / f
Now, to find the frequency for the n = 2 standing wave, we need to first find the wavelength for the n = 2 standing wave, denoted as λ2.
The relationship between the number of antinodes (n) and the wavelength (λ) in a standing wave is given by:
λn = 2λ / n
Substituting the given values, λ1 = 2λ / 1, we can find the wavelength (λ) for the n = 1 standing wave.
Then, we can find the wavelength (λ2) for the n = 2 standing wave using:
λ2 = 2λ / 2 = λ
Finally, we can find the frequency (f2) for the n = 2 standing wave using the formula:
f2 = v / λ2
To summarize, first, find the wavelength (λ) for the n = 1 standing wave using the formula λ = v / f. Then, use the wavelength (λ) to find the frequency (f2) for the n = 2 standing wave using the formula f2 = v / λ2.