Advertisements
Advertisements
Question
For the harmonic travelling wave y = 2 cos 2π (10t – 0.0080x + 3.5) where x and y are in cm and t is second. What is the phase difference between the oscillatory motion at two points separated by a distance of `(3λ)/4` (at a given instant of time)
Advertisements
Solution
Given, wave functions are y = 2 cos 2π (10t – 0.0080x + 3.5)
= 2 cos(20πt – 0.016πx + 7π)
Now, the standard equation of a travelling wave can be written as y = a cos(ωt – kx + `phi`)
On comparing with the above equation, we get
a = 2 cm
ω = 20π rad/s
k = 0.016π
Path difference = 4 cm
Δ`phi = (2π)/λ xx (3λ)/4 = (3π)/2` rad
APPEARS IN
RELATED QUESTIONS
As you have learnt in the text, the principle of linear superposition of wave displacement is basic to understanding intensity distributions in diffraction and interference patterns. What is the justification of this principle?
Consider two waves passing through the same string. Principle of superposition for displacement says that the net displacement of a particle on the string is sum of the displacements produced by the two waves individually. Suppose we state similar principles for the net velocity of the particle and the net kinetic energy of the particle. Such a principle will be valid for
A tuning fork of frequency 480 Hz is used to vibrate a sonometer wire having natural frequency 410 Hz. The wire will vibrate with a frequency
A 4⋅0 kg block is suspended from the ceiling of an elevator through a string having a linear mass density of \[19 \cdot 2 \times {10}^{- 3} kg m^{- 1}\] . Find the speed (with respect to the string) with which a wave pulse can proceed on the string if the elevator accelerates up at the rate of 2⋅0 m s−2. Take g = 10 m s−2.
A heavy ball is suspended from the ceiling of a motor car through a light string. A transverse pulse travels at a speed of 60 cm s −1 on the string when the car is at rest and 62 cm s−1 when the car accelerates on a horizontal road. Find the acceleration of the car. Take g = 10 m s−2
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 place, (b) if the two waves were produced at the same instant but first one was produced a distance 4⋅0 cm behind the second one? (c) If each of the waves has an amplitude of 2⋅0 mm, what would be the amplitudes of the resultant waves in part (a) and (b) ?
If `sqrt("A"^2+"B"^2)` represents the magnitude of resultant of two vectors `(vec"A" + vec"B")` and `(vec"A" - vec"B")`, then the angle between two vectors is ______.
Three identical charges are placed on three vertices of a square. If the force acting between q1 and q2 is F12 and between q1 and q3 is f13 then `"F"_13/"F"_12` = ____________.
Two particles P and Q describe simple harmonic motions of same amplitude a, frequency v along the same straight line. The maximum distance between the two particles is a`sqrt(2)`. The initial phase difference between the particles is
The displacement of an elastic wave is given by the function y = 3 sin ωt + 4 cos ωt. where y is in cm and t is in second. Calculate the resultant amplitude.
For the harmonic travelling wave y = 2 cos 2π (10t – 0.0080x + 3.5) where x and y are in cm and t is second. What is the phase difference between the oscillatory motion at two points separated by a distance of 4 m.
For the harmonic travelling wave y = 2 cos 2π (10t – 0.0080x + 3.5) where x and y are in cm and t is second. What is the phase difference between the oscillatory motion at two points separated by a distance of 0.5 m
For the harmonic travelling wave y = 2 cos 2π (10t – 0.0080x + 3.5) where x and y are in cm and t is second. What is the phase difference between the oscillatory motion at two points separated by a distance of What is the phase difference between the oscillation of a particle located at x = 100 cm, at t = T s and t = 5 s?
The equations of two waves are given by :
y1 5 sin2π (x - vt) cm
y2 3 sin2π (x - vt + 1.5) cm
These waves are simultaneously passing through a string. The amplitude of the resulting wave is ______.
In Young's double-slit experiment, the intensity at a point where the path difference is `lambda/4` is l. If the maximum intensity is l0, and then the ratio of `l_0/l` is ______.
`(cos45^circ = 1/sqrt2 = sin45^circ)`
When two coherent monochromatic light beams of intensities I and 4I are superimposed, then what are the maximum and minimum possible intensities in the resulting beams?
