The figure above represents a log-log plot of variable y versus variable x. The origin represents the point x = 1 and y = 1. Which of the following gives the approximate function relationship between y and x?
- y = 6 √x
- y = 6 x + 0.5
- y = 6 x2
- y = ½ x + 6
- y = ⅙ x2
In linear plots, the function y = b xm looks like a curved line (wghere m is the slope, b is the y-intercept). On log-log plots, that same function would look like a straight line.
The answer is A
Two experimental techniques determine the mass of an object to be 11 ± 1 kg and 10 ± 2 kg. These 2 measurements can be combined to give a wieghted average. How many kilograms is the uncertainty of the weighted average?
If we have N separate measuremnts of a quantity x
In an experimental observation of the photoelectric effect, the stopping potential was plotted versus the light frequency. The best straight line was fitted to the experimental points. Which of the following gives the slope of the line? (The workfunction of metal is φ)
- φ / e
- e / φ
- h / e
- e / h
- h / φ
Two sinsusoidal waveforms of the same frequency are displayed on an oscilloscope screen. The horizontal sweep of the oscilloscope is set to 100ns/cm and the vertical gains of channels 1 and 2 are each set to 2 V/cm. The zero-voltage level of each channel is given at the right in the figure. What is the approximate phase difference between the two waveforms?
Five classes of students measure the height of a building. Each class uses a different method and each measures the height many different times. The data for each class are plated below. Which class made the most precise measurement?
A student makes 10 one-second measurements of the disintegration of a sample of a long dived radioactive isotope and obtains the following values:
How long should the student count to establish the rate to an uncertainty of 1%?
The gain of an amplifier is plotted vs. angular frequency ω in the diagram above. If K and a are positive constants, the frequency dependence of the gain near ω = 3 x 105 second-1 is most accurately expressed by
- Ke-a ω
- K ω2
- K ω
- K ω-1
- K ω-2
This is a log-log graph. It cannot be an exponential relation, since the Gain would decrease exponentially as ω increases. It's not decaying nearly as fast.
The key phrase is "most accurately expressed". Choice (E) works because it applies decently well to the following two key points, one of them given, and the other one right next to the given:
Try a power-law relation:
The outputs of 2 electrical oscillators are copared on an oscilloscope screen. The oscilloscope spot is initially at the center of the screen. Oscillator Y is connected to the vertical terminals of the oscilloscope and oscillator X to the horizontal terminals. Which of the following patterns could appear on the scilloscope screen if the frequency of oscillator Y is twice that of oscillator X?
Problem 9In transmitting high frequency signals on a coaxial cable, it is important that the cable be terminated at an end with its characteristic impedance in order to avoid
- attenuation of the signal propagating in the cable
- reflection of signals from the terminated end of the cable
- overheating of the cable
- leakage of the signal out of the cable
- production of image currents in the outer conductor
A radioactive nucleus decays, with the activity shown inthe graph above. What is the half-life of the nucleus?
An attractive one-dimensional square well has depth V0. Which of the following best shows a possible wave function for a bound state?
The magnitude of the force F on an object can be determined by measure both the mass m of an object an dthe magnitude of its acceleraiton a, where F = ma. Assume that these measurements are uncorreleated and normally distributed. If the standard deviations of the measurements o fthe mass and the acceleration are σm and σa, respectively, then what is σF/F?
In laboratory experiments, graphs are employed to determine how one measured variable depends on another. These graphs generally fall into 3 categories: linear, semilog (largarithmic vs. linear) and log-log. Which type of graphic listed in the 3rd column below would NOT be the best for plotting data to test the relationship given in the 1st and 2nd columns?
A beam of neutral hydrogen atoms in their ground state is moving into the plane of this page and passes through a region of a strong inhomogeneous magnetic field that is directed upward in the plane of hte page. After the beam a passes through this field, a detector would find that it has been
- decreased voltage gain
- increased stability
- increased amplification
- decreased distortion
- increased bandwidth