# Homework Help: Error propagation for value not directly measurable

1. Jun 29, 2012

### sunrah

1. The problem statement, all variables and given/known data
This should be very simple:
Given the following (boundary frequency for photoelectric effect):

$\nu = \frac{\phi}{h}$

what would be the error on $\nu$?

2. Relevant equations
3. The attempt at a solution

$\varphi$ and h are both determined through linear regression (y = mx + c). Where

h =em and $\varphi = -ec$. The errors on m and c are supplied courtesy of computer software.

My understanding is that the product/division rule for error propagation can be used:

$\delta \nu = \nu\sqrt{(\frac{\delta \varphi}{\varphi})^{2}+(\frac{\delta h}{h})^{2}}$

my instructor disagrees

Last edited: Jun 29, 2012
2. Jul 1, 2012

### vela

Staff Emeritus
Sounds right to me. What's your instructor's idea for how to propagate the error?

3. Jul 2, 2012

### sunrah

well, i spoke to her now and she says that the systematic error on the voltage (digital multimeter) should be included.

$eU = h\nu + \varphi$ (1)

where $\varphi$is the work function.
The boundary frequency is given as $\nu_{b} = \frac{\varphi}{h}$ (2)

Of course we can write the $\nu_{b}$ in terms of voltage using (1), but we determined $\varphi$ and $h$ using linear regression which also supplied the standard error on those values. I'm not really sure how to determine the errors on $\nu_{b}$ now. Should I ignore the error on $\varphi$, combine (1) and (2) and just use the error for the voltage provided by the multimeter manufacturer?

$\delta \nu_{b} = \nu_{b} \sqrt{(\frac{\delta h}{h})^2 + (\frac{\delta U}{U})^2}$