AP Physics 1 Exam Question: Interference and Standing Waves

Question:

Two coherent sources, A and B, emit waves with an initial phase difference of 30°. The waves have a frequency of 500 Hz and travel in the same medium.

a) If the distance between the two sources is 2.0 m, calculate the path length difference (PLD) between the two waves at a point P located 5.0 m away from source A.

b) Determine whether constructive or destructive interference will occur at point P.

c) If the source A is producing waves with an amplitude of 0.10 mm and the sources are in phase at point P, calculate the amplitude of the resultant wave at point P.

Answer:

a) To find the path length difference (PLD) between the two waves at point P, we can use the formula:

PLD = r2 - r1

Where r1 is the distance from source A to point P, and r2 is the distance from source B to point P.

Given:

Distance between the two sources (AB) = 2.0 m Distance from source A to point P (r1) = 5.0 m

Since the two sources are in phase, the distance from source B to point P (r2) will be equal to the distance between the sources minus the distance from source A to point P:

r2 = AB - r1 = 2.0 m - 5.0 m = -3.0 m

Note: The negative sign indicates that source B is 3.0 m behind point P.

Therefore, the path length difference (PLD) is:

PLD = r2 - r1 = -3.0 m - 5.0 m = -8.0 m

b) To determine whether constructive or destructive interference will occur at point P, we need to consider the phase difference between the two waves.

Given: Initial phase difference between sources A and B = 30°

Constructive interference occurs when the phase difference is a multiple of 360°, while destructive interference occurs when the phase difference is an odd multiple of 180°.

The initial phase difference between sources A and B is 30°, which is not a multiple of 360° or an odd multiple of 180°. Therefore, neither constructive nor destructive interference will occur at point P.

c) To calculate the amplitude of the resultant wave at point P, we can use the principle of superposition. Since the two waves are in phase at point P, the amplitudes will simply add up.

Given: Amplitude of wave from source A = 0.10 mm

Therefore, the amplitude of the resultant wave at point P will be:

Amplitude of resultant wave = Amplitude of wave from source A + Amplitude of wave from source B = 0.10 mm + 0 mm (as there is no wave from source B due to destructive interference) = 0.10 mm

Thus, the amplitude of the resultant wave at point P is 0.10 mm.