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 4 m.
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
Phase difference Δ`phi = (2π)/λ` × Path difference
∴ Δ`phi` = 0.016π × 4 × 100 ......`(∵ (2π)/λ = k)`
= 6.4π rad
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?
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 240 Hz. The wire will vibrate with a frequency of
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
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 ____________.
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 ______.
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 ______.
Consider a ray of light incident from air onto a slab of glass (refractive index n) of width d, at an angle θ. The phase difference between the ray reflected by the top surface of the glass and the bottom surface is ______.
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 `λ/2`
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 ______.
