When considering interference between sound waves, we must look at the amplitudes of the waves. There are two types of interference: constructive and destructive.
1. Constructive Interference: This occurs when the amplitudes of two waves add together, resulting in a larger amplitude. It happens when the waves are in phase (i.e., their peaks and troughs align).
2. Destructive Interference: This occurs when the amplitudes of two waves cancel each other out (subtract from each other), resulting in a smaller amplitude or complete cancellation. It happens when the waves are out of phase (i.e., the peak of one wave aligns with the trough of another).
### Step-by-Step Solution:
1. Determine the Amplitudes of Both Waves:
- Amplitude of the first wave ([tex]\(A_1\)[/tex]) = 0.5
- Amplitude of the second wave ([tex]\(A_2\)[/tex]) = -0.75
2. Calculate the Resultant Amplitude:
To find the resultant amplitude ([tex]\(A_r\)[/tex]), we add the amplitudes of the two waves:
[tex]\[
A_r = A_1 + A_2 = 0.5 + (-0.75)
\][/tex]
3. Perform the Calculation:
[tex]\[
A_r = 0.5 - 0.75 = -0.25
\][/tex]
4. Determine the Type of Interference:
- If [tex]\(A_r\)[/tex] were positive or greater than the absolute value of both [tex]\(A_1\)[/tex] and [tex]\(A_2\)[/tex], it would indicate constructive interference.
- If [tex]\(A_r\)[/tex] were exactly zero, it would indicate complete destructive interference.
- Since [tex]\(A_r\)[/tex] is negative and smaller in absolute value compared to either [tex]\(A_1\)[/tex] or [tex]\(A_2\)[/tex], it indicates partial destructive interference.
Given the result that the resultant amplitude ([tex]\(-0.25\)[/tex]) is less than the amplitudes of the individual waves, we conclude that destructive interference occurs.
### Justification:
- The resulting amplitude is smaller than either of the initial amplitudes.
- This reduction in amplitude signifies that the waves are partially canceling each other out, characteristic of destructive interference.
Thus, at this single point in time where the sound waves combine, destructive interference occurs.
