# wave beats

• Sep 28th 2010, 08:53 PM
amma0913
wave beats
Wave beats occur when two waves have frequencies that are close but not identical. Start with the expressionsin(w1t)+sin(w2t),where w1~ w2 and w1-w2 is not equal to 0. From this expression, it probably is not obvious why wave beats occur. Can you derive an expression that is equal to the one given but much more useful in accounting for the
presence of wave beats? (Hints: sin(A + B) = sin(A)cos(B) + cos(A)sin(B), cos("A) = cos(A), and sin("A) = "sin(A).)

Thanks for the help!
• Sep 29th 2010, 05:53 AM
mr fantastic
Quote:

Originally Posted by amma0913
Wave beats occur when two waves have frequencies that are close but not identical. Start with the expressionsin(w1t)+sin(w2t),where w1~ w2 and w1-w2 is not equal to 0. From this expression, it probably is not obvious why wave beats occur. Can you derive an expression that is equal to the one given but much more useful in accounting for the
presence of wave beats? (Hints: sin(A + B) = sin(A)cos(B) + cos(A)sin(B), cos("A) = cos(A), and sin("A) = "sin(A).)

Thanks for the help!

More hints:

sin(A + B) = sin(A)cos(B) + cos(A)sin(B)

sin(A - B) = sin(A)cos(B) - cos(A)sin(B)

Therefore sin(A + B) + sin(A - B) = 2 sin(A) cos(B) .... (1)

Let A + B = w1t .... (2)

Let A - B = w2t .... (3)

Solve (2) and (3) for A and B in terms of w1t and w2t and substitute into the rigt hand side of (1):

sin(w1t) + sin(w2t) = ....