Two small loudspeakers emit sound waves of the same amplitude and frequency in phase with each other. The waves produce an interference pattern such that the distance from the right bisector to a point P on the third nodal line is x3. The wavelength of the sound is increased by a factor of 4. What is the new distance?
1) 1/4 x3
2) x3
3) 4 x3
4) 8 x3
again, what is "right bisector"? How can wavelength be increased?
This is the multiple choice given to me. I was stuck too. Any idea what would be the answer from 4 multiple choice
If the wavelength is quadrupled, so is the spacing. Increase wavelength by decreasing frequency.
To solve this problem, we need to understand the concept of interference patterns and nodal lines.
Interference occurs when two or more waves overlap and combine. In the case of sound waves, interference can result in regions where waves reinforce each other (constructive interference) or cancel each other out (destructive interference). Nodal lines are the regions of destructive interference where the waves cancel each other out.
Given that the two small loudspeakers emit sound waves of the same amplitude and frequency in phase with each other, we can assume that they are producing a standing wave pattern. In a standing wave pattern, the nodes are the regions of destructive interference.
Now, let's consider the situation. The distance from the right bisector to a point P on the third nodal line is given as x3. This means that point P is located at the third destructive interference point on the right side of the interference pattern.
Next, we are told that the wavelength of the sound is increased by a factor of 4. This means that the distance between consecutive nodal lines will also increase by a factor of 4.
Therefore, the new distance between the right bisector and point P on the third nodal line will be 4 times the original distance (x3). Hence, the correct answer is option 3) 4 x3.