Question

Two waves travel in the same direction along a string and interfere. The waves have the same wavelength and travel with the same speed. The amplitude of each wave is 19.7 mm and there is a phase difference of 110o between them. (a) what is the amplitude of the combined wave resulting from the interference of the two waves? (b) to what value should the phase difference be changed so that the combined wave will have an amplitude equal to that of one of the original value?​

Answer 1

Answer:

Answer

Let A be the amplitude of each wave. Thus the waves are

y

1

=Acos(ωt−kx)

and y

2

=Asin(ωt−kx)

Thus the net wave is y=y

1

+y

2

=Acos(ωt−kx)+Asin(ωt−kx)

=

2

Asin(ωt−kx+

4

π

)

Thus the new amplitude is

2

A=5.66cm=5.66×10

−2

m

Thus, x=2.