PHYS 101 Lecture Notes - Lecture 11: Standing Wave, Molecular Motor, Coin Flipping
15 May 2018
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Phys 101: Tutorial 12. Standing Waves and Diffusing things
Instructions: Print and bring with you to your tutorial. Read it over, but do NOT work on until your
tutorial time. Bring a calculator.
Standing Waves: (Take 25 mins max for this part)
for a string of length L:
and the wave speed is
where T is the
tension in the string and m is the mass of the string.
Question 1:
The figure below shows a standing wave on a string that has a certain frequency, f.
a) Copy the scale in the figure and then draw a standing wave with a frequency
of 2f / 3 for the same string.
b) Copy the scale again and draw a standing wave of frequency 3f /2 for the same string.
c) Can there be a standing wave if the frequency is changed to f /4? Explain why or why not.
Question 2:
The figure below shows a standing wave on a string with tension T.
a) Copy the scale below and draw a standing wave with the same frequency, but with a string
tension of 4T.
b) Can there be a standing wave if the tension is set to 2T and the frequency
is not changed? Explain why or why not.
Diffusion: 1D Random Walk (Take 25 mins to collect data, analysis can be done at home):
In Physics, we model a diffusing particle as an object undergoing a ‘random walk’. What this means is
that we have a walker who takes a step of a fixed size at regular intervals of time (this represents the
typical distance the particle goes before it makes a collision). Now the direction of this step is
completely random, and if our walker is confined to walk just in one dimension, that means they go
forward 50% of the time and backward 50% of the time. Now diffusion involves not just 1 walker, but
many, many walkers all doing exactly the same thing independently, each one taking random steps.
After a given number of steps, we can calculate the average position of all the walkers and other such
statistical quantities, like standard deviation/variance.
