1. Standing Waves Work Sheet
There are three hallways, two that are completely closed (A and C) and one with an opening on one side
(B). Hallway A and B both have the same length while C has half the length of A.
1. Rank the hallways in terms of fundament frequencies assuming there is a sound produced in each
hallway (smallest to largest)
a) A < B < C
b) C < B < A
c) C < A = B
d) B < A < C
2. Rank the hallways in terms of the wavelength of the fundamental mode. (smallest to largest)
a) A < B < C
b) C < B < A
c) C < A < B
d) B < A < C
3. If the wave length of the third harmonic in hallway C is measured to be 20m, then what is the frequency
of the second harmonic in hallway A?
2. Solutions:
1. d
Since we know the fundamental frequency with both ends closed is equal
to v/2L, and the fundamental frequency with one side open is v/4L we
can see that f(a)= v/(2L), f(b)= v/(4L), and f(c) = v/L
2. c
Hallway A λ = 2L , Hallway B λ = 4L , Hallway C λ = L
3. 5.72hz
λ = 20m = 2L/3
L(c) = 30m
L(a) = 2*30m = 60m
Frequency of the second harmonic can be calculated by v/L
So (343 m/s) / (60m) = 5.72hz
