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 `λ/2`
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 (λ/2)` = π rad .....[∵ Path difference = λ/2]
APPEARS IN
RELATED QUESTIONS
Light waves each of amplitude "a" and frequency "ω", emanating from two coherent light sources superpose at a point. If the displacements due to these waves are given by y1 = a cos ωt and y2 = a cos(ωt + ϕ) where ϕ is the phase difference between the two, obtain the expression for the resultant intensity at the point.
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 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) ?
The energy in the superposition of waves ____________.
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 wavelength of light used in young.'s double slit experiment is λ. The intensity at a point on the screen is I where the path difference is λ/6. If I0 denotes the maximum intensity, then the ratio of I and I0 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.
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?
