- #1
Von Neumann
- 101
- 4
Problem:
The problem asks to find which frequencies a listener, whom is receiving sound waves in the same direction from two variable-frequency speakers 50ft and 55ft away, will not hear anything at all.
Solution (so far):
My approach is to find an expression for the wave coming from each speaker, add them, and find when the sum equals 0. Doing so I get,
y_1=y_m*sin(k(x-x_0)-wt) [for speaker #1]
y_2=y_m*sin(k(x+x_0)-wt) [for speaker #2]
(where x_0=2.5 ft., y_m is the amplitude of the waves, k is the wave number, x is the position of the observer, w is the angular frequency, and t is the time)
For the next part, I know that the sum is
y_1+y_2=2*y_m*cos(k*x_0)sin(kx-wt)
However I am unable to get this answer using the my expressions for y_1 & y_2. Any suggestions?
The problem asks to find which frequencies a listener, whom is receiving sound waves in the same direction from two variable-frequency speakers 50ft and 55ft away, will not hear anything at all.
Solution (so far):
My approach is to find an expression for the wave coming from each speaker, add them, and find when the sum equals 0. Doing so I get,
y_1=y_m*sin(k(x-x_0)-wt) [for speaker #1]
y_2=y_m*sin(k(x+x_0)-wt) [for speaker #2]
(where x_0=2.5 ft., y_m is the amplitude of the waves, k is the wave number, x is the position of the observer, w is the angular frequency, and t is the time)
For the next part, I know that the sum is
y_1+y_2=2*y_m*cos(k*x_0)sin(kx-wt)
However I am unable to get this answer using the my expressions for y_1 & y_2. Any suggestions?
Last edited: