Generation of sound with Matlab Vibes and Waves in Action University of Massachusetts Lowell March 5, 2009

What have we learned in the last class? What are beats? How are beats generated? What are the two main characteristics of beats? Can you explain them?

What is Matlab? What are some programming languages? What can programming language be used for? Matlab is a scripting language that is often used to solve scientific and mathematical problems both numerically and through visual display. Matlab can be used for: – Calculations – 2D and 3D plotting – Symbolic manipulation of equations – Advanced animation and GUI tools

3D Sample plots

Matlab fundamentals What is a variable ? – Variable is a place where we store a piece of information. Example : Storing your friend’s phone number in your cell phone. – In Matlab variable names can include letters or numbers Example: nwave,T1,Kenergy,Force1,… Arithmetic Operations – Operators :+,-,*,^,/ – Example Ek=1/2 mv 2 In Matlab: Ek=1/2*m*v^2; List – In additions to doing operations on a single number, Matlab allows us to perform operations on a list of numbers. – One way to create a list is by using a colon notation t=begin:interval:end Example: t=300:10:350 this means that t={300,310,320,330,340,350}

Generating plots on Matlab To plot two variables x and y use command plot(x,y); If x and y are defined as x=1:1:8; and y=50:5:85; Label and titles can be added by using commands: xlabel(‘Time of the day [hr]’) ylabel(‘Temperature [F]’) title(‘Change of temperature during a day’)

Generate a wave using Matlab Generate t from 0 to 1 seconds (fs=44100) t=0:1/fs:1; Generate a wave with a frequency f=1000Hz f=1000; y=sin(2*pi*f*t); Plot generated wave plot(t,y); Listen to generated waves sound(y,fs);