Ep Exam Stuff > Engp_exam Qs_04

UNIVERSITY OF SOUTH AUSTRALIA Applied Physics - School of Electrical & Information Engineering ENGINEERING PHYSICS EXAM 2004 SECTION B - PRAC PROBLEM TRIGONOMETRIC RELATIONS a.b = ab cos θ In any triangle a2 = b2 + c2 − 2bc cos α C = 2π r A = π r2 UNCERTAINTY RELATIONS When y = axn : ∆y/y = n ∆x/x When y = axz or y = ax/z : ∆y/y = ∆x/x + ∆z/z

1. (a) In the analysis of data it is often informative to plot the data in one of the three ways indicated below. y

logny

logny

x

(A) linear-linear plot

x

(B) log-linear plot

lognx

(C) log-log plot

Figure 1 - Different plot formats. Lognx is log to the base n, and if to the base e, we call it the natural log of x, i.e. logex =n x (i) If you plot data on a linear-linear plot as in (A) and the result is a straight line, what does this tell you about the functional relationship describing the data? ……………………………………………………………………………………………………………… ……………………………………………………………………………………………………………… ……………………………………………………………………………………………………………… (ii) If you plot the natural log of the data (n y) vs x (i.e. a log-linear plot) as in (B) and the result is a straight line, what does this tell you about the functional relationship describing the data? ……………………………………………………………………………………………………………… ……………………………………………………………………………………………………………… ……………………………………………………………………………………………………………… (iii) If a log-log plot as in (C) results in a straight line relationship, what does this tell you about the functional relationship between y and x? ……………………………………………………………………………………………………………… ……………………………………………………………………………………………………………… ………………………………………………………………………………………………………………

In an acoustics experiment you measure the wavelength of a sound wave to be 33.0 ± 0.5 mm. You record the frequency of your acoustic source with an expensive precision frequency meter to be 10 400.00 Hz.

(b) (i)

What is the percentage relative error in the wavelength and frequency? ……………………………………………………………………………………………………………… ……………………………………………………………………………………………………………… ……………………………………………………………………………………………………………… ……………………………………………………………………………………………………………… ……………………………………………………………………………………………………………… ……………………………………………………………………………………………………………… ………………………………………………………………………………………………………………

(ii) Calculate the speed of the sound wave and its associated uncertainty. Hint: If you are unsure of the equations, all the equations required are in the formula list. ……………………………………………………………………………………………………………… ……………………………………………………………………………………………………………… ……………………………………………………………………………………………………………… ……………………………………………………………………………………………………………… ……………………………………………………………………………………………………………… ……………………………………………………………………………………………………………… ………………………………………………………………………………………………………………

(c) You may know from lectures that the temperature affects the resistance of conducting materials. The relationship is described by the equation R(T) = R0[1+α(T-T0)] where R is the resistance, T the temperature in either kelvin or degrees celsius and α is the temperature coefficient of resistivity of the material that the resistor is made out of. You make some measurements of the resistance of a device using facilities at your disposal ie. at liquid nitrogen temperature (-210 oC), room temperature and in boiling water. You plot the data and the following graph results.

Resistance data for unknown alloy 92 91.5 R(Ω) 91 90.5 90 89.5 89 -200

-100

0

100

200

o

T( C)

(i)

Calculate the temperature coefficient of resistivity at 20oC for this unknown alloy. ……………………………………………………………………………………………………………… ……………………………………………………………………………………………………………… ……………………………………………………………………………………………………………… ……………………………………………………………………………………………………………… ……………………………………………………………………………………………………………… ……………………………………………………………………………………………………………… ………………………………………………………………………………………………………………