Practice Interference in Physics

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

Quick Recap

The phenomenon that occurs when two or more waves overlap in space, combining their displacements at every point according to the principle of superposition.

When waves meet, they add up or cancel out at each point depending on whether their crests and troughs align.

Showing a random 20 of 50 problems.

Example 1

easy
Two wave crests meet at a point. Is this constructive or destructive interference?

Example 2

medium
A double-slit experiment uses sodium light (λ=589 nm\lambda = 589\text{ nm}) with d=0.5 mmd = 0.5\text{ mm} and L=2.0 mL = 2.0\text{ m}. Find the distance from the central maximum to the 5th bright fringe.

Example 3

hard
A double-slit experiment uses white light. The central maximum is white, but the higher-order fringes show color separation. Why does the first-order red fringe appear farther from center than the first-order blue?

Example 4

hard
In a double-slit experiment, immersing the apparatus in water (n=1.33n=1.33) changes the fringe spacing. By what factor does the spacing change?

Example 5

medium
Two waves of wavelength 33 m have a path difference of 4.54.5 m. Constructive or destructive?

Example 6

easy
True or false: when two waves destructively interfere, the energy is destroyed.

Example 7

medium
Two identical waves of amplitude AA are exactly out of phase (half-wavelength offset). What is the combined amplitude?

Example 8

easy
Two speakers emit identical sound waves in phase. A listener stands equidistant from both speakers. Does the listener hear constructive or destructive interference? What about if one speaker is moved half a wavelength farther away?

Example 9

easy
Two identical pulses traveling in opposite directions on a string meet. At the instant they fully overlap, the string is flat. Were the pulses in phase or out of phase?

Example 10

easy
After two waves overlap and interfere, what happens to them as they continue past the overlap region?

Example 11

hard
Two coherent sources emit identical waves. If the slit separation dd is doubled while λ\lambda and LL stay fixed, what happens to the fringe spacing?

Example 12

medium
Two in-phase sources produce identical waves of amplitude AA. At point P the intensity is maximum. At point Q the path difference is λ3\tfrac{\lambda}{3}. What is the intensity ratio IQ/IPI_Q/I_P? (Use Icos2(ϕ/2)I \propto \cos^2(\phi/2).)

Example 13

easy
Does destructive interference destroy energy?

Example 14

hard
In a double-slit experiment with λ=500 nm\lambda=500\text{ nm}, d=0.20 mmd=0.20\text{ mm}, and L=1.0 mL=1.0\text{ m}, a thin glass slab (n=1.5n=1.5, thickness t=10μmt=10\,\mu\text{m}) is placed in front of one slit. By how many fringes does the central maximum shift?

Example 15

medium
Two speakers 4.0 m4.0\text{ m} apart emit a 680 Hz680\text{ Hz} tone in phase (sound speed 340 m/s340\text{ m/s}). A listener walks along a line 10 m10\text{ m} in front of the speakers, parallel to the line joining them. What is the spacing between adjacent quiet spots?

Example 16

challenge
Two coherent sources produce a path difference of 2.5λ2.5\lambda at a point. Classify the interference and state the phase difference in wavelengths.

Example 17

medium
Two waves of wavelength 44 m have a path difference of 66 m. Constructive or destructive?

Example 18

medium
In a double-slit experiment, light of wavelength 500 nm500 \text{ nm} passes through slits 0.2 mm0.2 \text{ mm} apart. A screen is 2 m2 \text{ m} away. What is the spacing between adjacent bright fringes?

Example 19

easy
Two coherent waves arrive at a point with a path difference of 00. What type of interference occurs?

Example 20

challenge
Two coherent sources of equal intensity produce a pattern with fringe visibility V=(ImaxImin)/(Imax+Imin)=1V = (I_{\max}-I_{\min})/(I_{\max}+I_{\min}) = 1. If one source is now attenuated so its amplitude is A/2A/2 while the other stays at AA, find the new visibility.