Ch 16: Waves & SoundSee all chapters
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Wave Interference

See all sections
Sections
What is a Wave?
The Mathematical Description of a Wave
Waves on a String
Wave Interference
Standing Waves
Sound Waves
Standing Sound Waves
Sound Intensity
The Doppler Effect
Beats

Concept #1: Wave Interference

Practice: In the following figure, two interfering waves are drawn at some instance in time. 

a. Indicate the regions on the graph where constructive interference occurs.
b.Indicate the regions on the graph where destructive interference occurs.

Concept #2: Wave Reflection

Additional Problems
The following figure shows successive wavefronts emitted by two different speakers. Identify the points of constructive interference between the two waves by indicating them on the figure. Note that the time indicated in each figure is how long ago that wave front was emitted. Ignore constructive interference between two wave troughs, because their positions aren't indicated in the figure.
Two waves are oscillating on the same string, with the equations y1(x,t) = (1.5 cm)sin((1.2 s-1)t - (5.2 m-1)x) y2(x,t) = (5.2 cm)sin((2.3 s-1)t - (2.3 m-1)x) What will the displacement of the string be at x = 3 m and t = 5 s?
A wave on a string propagates down a 150 g, 4 cm long string with a 10 cm wavelength before encountering a transition to a new string. If the new string is 250 g in mass and 8 cm long, and both strings have a tension of 100 N, (a) What is the wavelength of the wave that reflects off the transition point between the two strings? (b) What is the wavelength of the wave that passes through the transition point between the two strings?
Two harmonic waves are described by y1 = A sin(3 x - 5 t), y2 = A sin(3 x - 5 t - 4), where A = 22 m, with x and t being given in SI units and the phase angles in radians. What is the displacement of the wave produced by interference of these two waves at x = 1 m, t = 1 s?
Two loudspeakers emit sound waves along the x-axis. The sound has a maximum intensity when the speakers are 24 cm apart. The sound intensity decreases as the distance between the speakers is increased, reaching zero at a separation of 30 cm. (a) What is the wavelength of the sound? (b) If the distance between the speakers continues to increase, at what separation will the intensity next again be a maximum?
Antennas A and B emit coherent radio waves that have wavelength 8.0 m and that are in phase. Point P is on the line connecting the two antennas and is 9.0 m from A and 17.0 m from B. Is the interference at point P for the waves from the two antennas constructive or destructive?(a) destructive(b) constructive 
Antennas A and B emit coherent radio waves that have wavelength 8.0 m and that are in phase. Antenna B is 4.0 m to the right of antenna A and point P is 4.0 m to the right of antenna B. Is the interference at point P for the waves from the two antennas constructive or destructive?A) constructiveB) destructive