TPR Wave Question

[G1SG2]

In a given medium with fixed boundaries, the longest wavelength will set up a standing wave is 4 m. If waves propagate through the medium at 8 m/s, what is the LOWEST possible frequency associated with a standing wave within this medium?

A. 0.5 Hz
B. 1 Hz
C. 2 Hz
D. 4 Hz

I used f=nv/2L, 8/2(4)=8/8=1Hz and arrived at answer choice B but the explanation says:

The lowest harmonic-or fundamental-frequency, f1, corresponds to the longet harmonic-or fundamental-wavelength, lamda1. In this case, then, we find that f1=v/lamda1=(8 m/s)/ 4m=2 Hz.

I thought for standing waves with fixed ends, we were supposed to use f=nv/2L?

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[Dr Gerrard]

v = f * lambda

8/4 = 2

EDIT: L = lambda * n / 2 ---> lambda = 2 * L / n

v = f * lambda

f = v / lambda = v / (2 * L/n) = v * n / 2L ---> You have this right

But L =/= 4, it equals 2. Maximum wavelength is achieved at the fundamental harmonic, where n = 1. If you plug this in, you get L = 2.

f = 8 * 1 / 2*2 = 2

 

[G1SG2]

v = f * lambda

8/4 = 2

EDIT: L = lambda * n / 2 ---> lambda = 2 * L / n

v = f * lambda

f = v / lambda = v / (2 * L/n) = v * n / 2L ---> You have this right

But L =/= 4, it equals 2. Maximum wavelength is achieved at the fundamental harmonic, where n = 1. If you plug this in, you get L = 2.

f = 8 * 1 / 2*2 = 2

Thanks!