# If you start with two sinusoidal waves of the same amplitude traveling in phase on a string and...

## Question:

If you start with two sinusoidal waves of the same amplitude traveling in phase on a string and then somehow phaseshift one of them by 5.4 wavelengths, what type of interference will occur on the string?

(a) Intermediate (closer to fully constructive)

(b) Intermediate (closer to fully destructive)

(c) Fully destructive

(d) Fully constructive

## Constructive and Destructive Interferences:

Interference occurs when two coherent waves overlap. When two identical waves are in phase -- that is, crest-to-crest and trough-to trough -- their resultant shows constructive interference with double the amplitude of the original wave. On the other hand, when the incoming waves are out of phase -- that is, crest-to-trough or trough-to-crest-- the resultant shows destructive interference.

## Answer and Explanation: 1

Become a Study.com member to unlock this answer! Create your account

View this answerFor constructive interference between the two sinusoidal waves, they should be multiples of one wavelength.

For destructive interference between...

See full answer below.

#### Ask a question

Our experts can answer your tough homework and study questions.

Ask a question Ask a question#### Search Answers

#### Learn more about this topic:

from

Chapter 5 / Lesson 16Interference occurs when two waves meet. Explore the lesson and examples to learn about the differences between constructive and destructive interference.

#### Related to this Question

- Two waves of the same frequency and wavelength, moving in the same direction and each with amplitude A interfere with each other. The resulting wave also has an amplitude A, what is the phase difference of the component waves?
- Two identical sinusoidal transverse waves travel along a stretched string. Each wave has an amplitude y_m and wavelength \lambda. If the phase difference between the two waves is 0.20 \ \lambda, what is the amplitude of the resultant? a) 1.6 \ y_m b) 0.8
- Two waves traveling on a string in the same direction both have a frequency of 92 Hz, a wavelength of 0.19 m, and an amplitude of 0.32 m. What is the amplitude of the resultant wave if the original wa
- Two sinusoidal waves are identical except for their phase. When these two waves travel along the same string, for which phase difference will the amplitude of the resultant wave be a minimum?
- Two sinusoidal traveling waves are co-propagating along a string. They have the same frequency f, but different amplitudes {y1, y2} and phase angles {f1, f2}. (a) What is the largest possible amplitude of the resultant wave? For what phase difference (f2
- Two waves traveling on a string in the same direction both have a frequency of 100 Hz, a wavelength of 2 cm and an amplitude of .02 m. What is the amplitude of the resultant wave if the original waves
- (a) Two sinusoidal waves with the same amplitude, wavelength and period travel in the same direction to + x-axis along a string and interfere with each other. Assume the wave displacements are given as: y_1 = 2.2 sin (4x -12t) m and y_2 = 2.2 sin (4x -12t
- Two waves are travelling on a string, in the same direction. Both have a frequency of 101Hz, a wavelength of 0.400m, and an amplitude of 0.410m. What is the amplitude of the resultant wave, if the ori
- Two waves of the same frequency have amplitudes 1.00 and 2.00. They interfere at a point where their phase difference is 60.0 degrees. What is the resultant amplitude?
- Two waves traveling on a string in the same direction both have a frequency of 92 Hz, a wavelength of 0.19 m, and an amplitude of 0.32 m. a. What is the amplitude of the resultant wave if the original
- Two coherent EM waves have amplitudes of E0 and 0.370 E0. What is the resulting amplitude when they interfere destructively?
- Two waves having the same frequency, wavelength, and amplitude are traveling in the same direction. If they differ in phase by \pi /3 and each has an amplitude of 0.040 m, what is the amplitude of the
- Consider two waves interfering with one another. What happens to the amplitude of the resulting wave if the phase difference between the two initial waves is 6 pi?
- What phase difference between two otherwise identical traveling waves, moving in the same direction along a stretched string, will result in the combined wave having an amplitude of 1.4 times that of the common amplitude of the two combining waves? Expres
- Two sinusoidal waves of the same frequency travel in the same direction along a string. If ym1=3.1cm, ym2=4.4cm, varphi 1=0, and varphi 2=pi/4 rad, what is the amplitude of the resultant wave?
- What phase difference between two otherwise identical traveling waves, moving in the same direction along a stretched string, will result in the combined wave having an amplitude 1.55 times that of the common amplitude of the two combining waves (in degre
- What phase difference between two otherwise identical traveling waves, moving in the same direction along a stretched string, will result in the combined wave having an amplitude 0.52 times that of the common amplitude of the two combining waves? Express
- What phase difference, between two otherwise identical traveling waves, moving in the same direction along a stretched string, will result in the combined wave, having an amplitude 1.7 times that of the common amplitude of the two combining waves? Express
- What phase difference between two otherwise identical traveling waves, moving in the same direction along a stretched string, will result in the combined wave having an amplitude 1.55 times that of the common amplitude of the two combining waves? Express
- Two waves traveling on a string in the same direction both have a frequency of 150 Hz, a wavelength of 2 cm, and an amplitude of 0.06 m. What is the amplitude of the resultant wave if the original wav
- Two waves, each having a frequency of 100 Hz and a wavelength of 2.0 cm, are traveling in the same direction on a string. What is the phase difference between the waves (a) if the second wave was produced 0.015 s later than the first one at the same insta
- What phase difference between two identical waves, moving in the same direction along a stretched string, results in a combined wave having an amplitude 1.5 times?
- These two waves travel along the same string: y_1 = (4.17 mm) sin(2.24 \pi x - 300 \pi t), y_2 = (5.96 mm) sin(2.24 \pi x - 300 \pi t + 0.727 \pi rad). What are (a) the amplitude and (b) the phase angle (relative to wave 1) of the resultant wave? (c
- Two waves, each having a frequency of 100 Hz and a wavelength of 2.0 cm, are travelling in the same direction on a string. What is the phase difference between the waves (a) if the second wave was produced 0.015 s later than the first one at the same, pla
- What phase difference between two otherwise identical harmonic waves, moving in the same direction along a stretched string, will result in the combined wave having an amplitude 1.0 times that of the
- Two sinusoidal waves of the same wavelength travel in the same direction along a stretched string. For wave 1, ym = 4.0 mm and phi = 0; for wave 2, ym = 4.5 mm and phi = 90 degrees. (a) What is the amplitude of the resultant wave? (b) What is its phase co
- A sinusoidal transverse wave travels along a long stretched string. The amplitude of this wave is 0.0887 m, its frequency is 2.27 Hz, and its wavelength is 1.73 m. (a) What is the shortest transverse
- A sinusoidal transverse wave travels along a long stretched string. The amplitude of this wave is 0.0937 m, its frequency is 3.03 Hz, and its wavelength is 1.07 m. (a) What is the shortest transverse
- Two sinusoidal waves have the same angular frequency, the same amplitude y, and travel in the same direction in the same medium. If they differ in a phase by 60^o, the amplitude of the resultant wave is given by A. 0.5y B. 0.87y C. y D. 1.7y E.
- Three sinusoidal waves of the same frequency travel along a string in the positive direction of an x axis.Their amplitudes are y1, y1/2, and y1/4, and their phase constants are 0, π/2, and π,respectively. (a) What is the amplitude of the resultant
- Two sinusoidal waves with identical wavelengths and amplitudes travel in opposite directions along a string with speed v. If the time interval between instants when the string is flat is t, what is th
- If two sound waves undergo complete destructive interference, what must be true? A. They have the same amplitude. B. They have the same frequency. C. They are 180 degrees out of phase. D. all of the above
- Two identical waves traveling in the same direction are superimposed. What should be the phase difference between the waves for maximum destructive interference to occur?
- Two sinusoidal waves travel in the same direction and have the same frequency. Their amplitudes are Y_1 and Y_2. The smallest possible amplitude of the resultant wave is: a) Y_1 + Y_2 and occurs if they are 180^o out of phase b) [Y_1 - Y_2] and occurs i
- The velocity of a wave on a particular string is 21.8 m/s and the string is 3 meters long. What are the three lowest harmonic frequencies that will produce a standing wave?
- Two sinusoidal waves with identical wavelengths and amplitudes travel in opposite directions along a string with a speed of 12 cm/s. If the time interval between instants when the string is flat is 0.55 s, what is the wavelength of the waves?
- Two sinusoidal waves of the same wavelength travel in the same direction along a stretched string. For wave 1, ym = 3.5 mm and ? = 0; for wave 2, ym = 5.1 mm and ? = 73�. What are the (a) amplitude an
- Two waves are traveling in the same direction along a stretched string. The waves are 90.0 degrees out of phase. Each wave has an amplitude of 7.00 cm. Find the amplitude of the resultant wave.
- A sinusoidal transverse wave travels along a long stretched string. The amplitude of this wave is 0.0989 m, its frequency is 2.95 Hz, and its wavelength is 1.37m. a) What is the shortest transverse di
- A sinusoidal electromagnetic wave having a magnetic field of amplitude 1.90 \mu T and a wavelength of 408 nm is traveling in the +x direction through empty space. (a) What is the frequency of this wave? (b) What is the amplitude of the associated electr
- A sinusoidal wave travels along a string. The time for a particular point to move from maximum displacement to zero is 0.14 s. What are the (a) period and (b) frequency? (c) The wavelength is 2.4 m; w
- A sinusoidal wave is traveling along a rope. The oscillator that generates the wave completes 35.0 vibrations in 29.0 s. A given crest of the wave travels 440 cm along the rope in 12.0 s. What is the wavelength of the wave?
- A sinusoidal wave is traveling along a rope. The oscillator that generates the wave completes 37.0 vibrations in 29.0 s. A given crest of the wave travels 420 cm along the rope in 15.0 s. What is the wavelength of the wave?
- A sinusoidal wave is traveling along a rope. The oscillator that generates the wave completes 37.0 vibrations in 33.0 s. A given crest of the wave travels 420 cm along the rope in 15.0 s. What is the wavelength of the wave?
- Two identical traveling waves, moving in the same direction, are out of phase by \frac{\pi}{3} rad. What is the amplitude of the resultant wave in terms of the common amplitude y_m of the two combinin
- In a transverse wave on a string, the string oscillates: points on the string are displaced vertically from the equilibrium position. In a (transverse) electromagnetic wave, what is oscillating?
- Wave amplitude is related to what? a. wave velocity b. frequency c. energy d. wavelength
- Identical points on two harmonic waves with the same wavelength (0.65 meters) and frequency are separated by a distance of 0.15 meters. What is the phase difference between the waves?
- Identical points on two harmonic waves with the same wavelength (.65 meters) and frequency are separated by a distance of .15 meters. What is the phase difference between the waves?
- What will happen to the wavelength of a sinusoidal wave on a string if the tension in the string is increased while we keep the frequency of the wave the same? (a) The wavelength will stay the same. (b) The wave speed will increase. (c) The wavelength wil
- Waves are sent down a 2.00m long string pinned down at both ends setting up standing waves. The equation for these waves is given by, y(x,t) = (0.040m) sin (2pi x) cos (200pi t) Find: a) the amplitude of the original waves sent, b) frequency, c) wavele
- Two sinusoidal waves of the same period, with amplitudes of 4.5 and 8.0 mm, travel in the same direction along a stretched string; they produce a resultant wave with an amplitude of 9.1 mm. The phase constant of the 4.5 mm wave is 0. What is the phase con
- A transverse traveling sinusoidal wave on a string has a frequency of 100 Hz, a wavelength of 0.040 m, and an amplitude of 2.0 mm. What is the maximum acceleration at any point on the string?
- Draw two sine waves of equal amplitude and frequency, in phase, and add them graphically. What are the amplitude and the frequency of the sum wave?
- Two waves, both of amplitude A, are traveling in opposite directions along a rope. What is the range of displacement y that the two waves may cause when they overlap?
- Two sinusoidal waves of the same frequency travel in the same direction along a string. If ym1 = 4.2 cm, ym2 = 5.9 cm, 1 = 0, and 2 = /5 rad, what is the amplitude (in cm) of the resultant wave?
- Draw two component waves with phase differences of 45 degrees, 90 degrees and 180 degrees. What are the amplitude and frequency of each sum wave?
- A string that is fixed at both ends has a length of 2.21 m. When the string vibrates at a frequency of 83.3 Hz, a standing wave with three loops is formed. (a) What is the wavelength of the waves that
- The electric field of a sinusoidal electromagnetic wave obeys an equation. (A) What is the speed of the wave? (B) What is the amplitude of the electric field of this wave? (C) What is the amplitude of
- Two sinusoidal waves of the same period, with amplitudes of 8.0 mm and 11.5 mm, travel in the same direction along a stretched string. They produce a resultant wave with an amplitude of 18.190 mm. The
- A string along which waves can travel is 2.70 m long and has a mass of 260.0 g. The tension in the string is 36.0 N. What must be the frequency of travelling waves of amplitude 7.70 mm for the averag
- Two sinusoidal waves with identical wavelengths and amplitudes travel in opposite directions along a string with a speed of 19 cm/s. If the time interval between instants when the string is flat is 0.
- Two identical traveling waves, moving in the same direction, are out of phase by 5.0 rad. What is the amplitude of the resultant wave in terms of the common amplitude ym of the two combining waves? (
- A sinusoidal transverse wave is traveling on a string. Any point on the string: A) moves in the same direction as the wave. B) moves in simple harmonic motion with a different frequency than that of
- A standing wave is formed in a stretched string that is 3.0 m long. What are the wavelengths of (a) the first harmonic and (b) the second harmonic?
- A wave on a string has a wave function given by y (x, t) = (0.0210 m) sin [(6.91 m^{-1}) x + (2.38 s^{-1})t]. (a) What is the amplitude of the wave? (b) What is the period of the wave? (c) What is th
- Two waves, travelling in the same direction through the same region, have equal frequencies, wavelengths and amplitudes. If the amplitude of each wave is 4 mm and the phase difference between the waves is 90^{\circ}, what is the resultant amplitude?
- A string of length 2.7 m is fixed at both ends. When the string vibrates at a frequency of 90.0 Hz, a standing wave with 5 loops is formed. What is the wavelength of the waves that travel on the strin
- A sinusoidal wave travels along a string. The time for a particular point to move from maximum displacement to zero is 0.19 s. What are the (a) period and (b) frequency? (c) The wavelength is 1.0 m; what is the wave speed?
- A wave of amplitude 0.30 m interferes with the second wave of amplitude 0.20 m. What are the largest and smallest displacements that can occur? What type of interference is demonstrated by each displa
- Two identical traveling waves, moving in the same direction, are out of phase by pi/6.0 rad. What is the amplitude of the resultant wave in terms of the common amplitude ym of the two combining waves?
- By doubling the wavelength of a wave on a particular string, what happens to the wave speed v and the frequency f?
- A string vibrates with standing waves in 5 loops when the frequency is 600 Hz. What frequency will cause the string to vibrate in only two loops?
- The equation of a transverse wave traveling on a string is given. What is the amplitude? What is the frequency? What is the wave velocity? What is the wavelength? For the same wave, find the maximum t
- A transverse wave of frequency 30 Hz propagates down a string. Two points 25 cm apart are out of phase by \dfrac{\pi}{4}. \\ A.) What is wavelength of the wave? B.) At a given point, what is the phase difference (as a multiple of \pi) between two displac
- Two sinusoidal waves having the same frequency and travelling in the same direction are combined. If their amplitudes are 6.0 and 8.0 cm and have a phase difference of \pi/2 rad, determine the amplitude of the resultant motion.
- Standing waves on a 1.0-m-long string that is fixed at both ends are seen at successive frequencies of 36 Hz and 48 Hz. a. What is the fundamental frequency? b. What is the wave speed?
- 1) A sine wave is traveling along a string. The time for a particular point to move from maximum displacement to zero is 0.590 s. What is the period? 2) What is the frequency? 3) The wavelength is 1.
- A 2.8 \ m long string of mass 11.2 \ g is clamped at both ends. The tension in the string is 143 \ N. The string is plucked so that it oscillates. What is the wavelength and frequency of the resulting wave it produces a standing wave with two antinodes?
- Two identical traveling waves, moving in the same direction, are out of phase by \pi/3.0 rad. What is the amplitude of the resultant wave in terms of the common amplitude ym of the two combining waves
- A wave on a string is described by the following equation: y=(14cm)\cos(\frac{\pi}{5.1 cm}x-\frac{\pi}{14s}t) A) What is the amplitude of this wave? B) What is its wavelength? C) What is its period
- Two sinusoidal waves in a string are defined by the functions y_1= 2 sin (20x-32t), and y_2=2 sin (25x-40t) where y_1, y_2, and x are in centimeters and t is in seconds. What is the phase difference between these two waves at the point x=5 cm at t=2 s? (
- An oscillator creates periodic waves on a stretched string. a. If the period of the oscillator doubles, what happens to the wavelength and wave speed? 1. The wavelength is halved but the wave speed is unchanged. 2. The wavelength is unchanged but the wa
- A wave of amplitude 0.37 \ m interferes with a second wave of amplitude 0.18 \ m is traveling in the same direction. What is the largest resultant amplitude that can occur?
- Two identical sinusoidal waves with wavelengths of 2.00 m travel in the same direction at a speed of 2.00 m/s. The second wave originates from the same point as the first, but at a later time. The amplitude of the resultant wave is the same as that of eac
- Two identical waves (of equal amplitude and frequency) arrive in phase at a certain point A. The resultant wave at point A is A. a wave of the same frequency and amplitude as the two incoming waves.
- Two waves traveling along the same string are described by the following wave equations: y_1(t) = 3.0 sin(4x - 1.4t), \; y_2 (t) = 3.0 sin(4x - 1.4t + \pi/2). What is the amplitude of the resultant wave? a. 4.2 m b. 1.3 m c. 6.8 m d. 2.5 m e. 3.2 m
- A 2\ \mathrm{m} long string of mass 10\ \mathrm{g} is clamped at both ends.the tension in the string is 150\ \mathrm{N}. The string is plucked so that it oscillate. What is the wavelength and frequency of the resulting wave if it produces a standing wave
- A string is stretched 1.25 m between two points. It is observed to have successive resonant frequencies of 321 and 428 Hz. What is the lowest frequency for this string? What is the wave speed for the
- (a) What is the amplitude of the oscillation shown in the figure? (b) What is the frequency of this oscillation? (c) What is the phase constant?
- Describe what happens when waves reflect off a boundary. a) Amplitude. b) Frequency. c) Wave speed.
- Two 1-D waves of amplitude A and period T and constant phase phi are superposed. If wave 1 travels 13.5 wavelengths farther than wave 2, the interference is (A) constructive (B) destructive (c) partia
- a) What is the amplitude of this wave? b) What is the frequency of this wave? c) What is the wavelength of this wave?
- Standing waves on a 1.3 \ m long string that is fixed at both ends are seen at successive frequencies of 36 \ Hz and 54 \ Hz. (a) What is the fundamental frequency? (b) What is the wave speed?
- When interference happens with two monochromatic light waves, which of the following is a characteristic of the amplitude of the resultant wave? \\ a. it is zero. \\ b. it is equal to the sum of the a
- Three sinusoidal waves of the same frequency travel along a string in a positive direction of an x axis. Their amplitudes are y_{1}, y_{1}/2, and y_{1}/3, and their phase constants are 0, \pi/2, and \pi, respectively. What is the phase constant of the res
- A standing wave is moving at 300 m/s on a 6 m long string. What is the fundamental frequency of the wave?
- Consider a wave on a string that has an amplitude of 8 cm, a wavelength of 0.7 m and a propagation speed of 2.6 m/s. a) What is the period of this wave? b) What is the frequency of this wave?
- Two harmonic waves are described by y_1 = 5 \sin (6x - 900 t ) m \\ y_2 = 5 \sin (6x - 900 t - 2) m What is the wavelength of the resultant wave? a. 3 m b. 2 m c. 1 m d. 4 m e. 6 m