Question

Two waves of the same frequency interfere with each other. The first wave has amplitude A1 = 38 cm and wavelength λ1 = 3 m. The second wave has amplitude A2 = 31 cm and wavelength λ2 = 3 m. What is the amplitude of the sum of the two waves if the waves are exactly in phase?

Answer 1

The amplitude of the summed waves that are exactly in phase is the sum of their individual amplitudes, which is 69 cm for waves with amplitudes of 38 cm and 31 cm respectively.

Step-by-step explanation:

When two waves of the same frequency and wavelength interfere with each other, the resultant amplitude depends on their phase difference. In the case where the two waves are exactly in phase, we experience constructive interference, which means that their amplitudes will simply add up. Given the amplitudes A1 = 38 cm and A2 = 31 cm for the first and second wave respectively, and since both have the same wavelength of λ = 3 m and are in phase, the amplitude of the sum of these two waves will be the sum of their individual amplitudes.

The resulting amplitude AR, in the case of constructive interference where the waves are exactly in phase (phase difference is 0 degrees or 0 radians), is:

AR = A1 + A2
AR = 38 cm + 31 cm
AR = 69 cm

Hence, the amplitude of the summed wave is 69 cm.