3.3.2.1
Worked example: counting quiet spots from two speakers
Interference & Diffraction — AQA A-Level Physics
Worked Example
Two speakers play a 280 Hz note in phase. A student walks 3.0 m from speaker A towards speaker B. Speed of sound = 340 m/s. How many quiet spots are heard?
Show Solution
1
Calculate wavelengthThe minimum distance between two points on a wave that are in phase (e.g. crest to crest). Measured in metres (m).
$$\lambda = \frac{v}{f} = \frac{340}{280} = 1.2 \text{ m}$$
2
Find path differences for destructive interference
Destructive interference when path differenceThe difference in distance travelled by two waves from their sources to a given point. Determines whether constructive or destructive interference occurs. $= (n + \frac{1}{2})\lambda$:
- $n = 0$: path differenceThe difference in distance travelled by two waves from their sources to a given point. Determines whether constructive or destructive interference occurs. $= 0.6$ m
- $n = 1$: path differenceThe difference in distance travelled by two waves from their sources to a given point. Determines whether constructive or destructive interference occurs. $= 1.8$ m
- $n = 2$: path difference $= 3.0$ m
3
Count the quiet spots within 3.0 m
All three path differences (0.6, 1.8, 3.0 m) fall within the 3.0 m walk.
Answer
The student hears 3 quiet spots.