3- Two sinusodial waves of the same frequency are to be sent in the same directi

Question

3- Two sinusodial waves of the same frequency are to be sent in the same direction along a taut string. One wave has an amplitude of 5.0 mm, the other 8.0 mm. (a) What phase difference italic phi1between the two waves results in the smallest amplitude of the resultant wave? (b) What is that smallest amplitude? (c) What phase difference italic phi2results in the largest amplitude? (d) What is that largest amplitude? (e) What is the resulatnt amplitude if the phase angle is (italic phi1-italic phi2)/2?

Explanation / Answer

a] the phase difference for this should be pi or 180 degree (both the same thing)

b]that smallest amplitude

= sqrt [8^2 + 5^2 -2*8*5]

=3

c]for largest = 0 or 360 degree

d] amplitude = sqrt [8^2 + 5^2 + 2*5*8]

= 13

e]phase angle = pi-0/2 = pi/2

resultant ampolitude = sqrt [5^2 + 8^2 +0 ]

= 9.433

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