Advertisements
Advertisements
प्रश्न
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`
Advertisements
उत्तर
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
संबंधित प्रश्न
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.
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?
A sonometer wire having a length of 1⋅50 m between the bridges vibrates in its second harmonic in resonance with a tuning fork of frequency 256 Hz. What is the speed of the transverse wave on the wire?
Answer briefly.
State and explain the principle of superposition of waves.
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.
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 `(3λ)/4` (at a given instant of time)
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?
In the interference of two sources of intensities I0 and 9I0 the intensity at a point where the phase difference is `pi/2` is ______.
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 ______.
