Advertisements
Advertisements
प्रश्न
Explain why (or how) The shape of a pulse gets distorted during propagation in a dispersive medium.
Advertisements
उत्तर १
A pulse is actually is a combination of waves having different wavelengths. These waves travel in a dispersive medium with different velocities, depending on the nature of the medium. This results in the distortion of the shape of a wave pulse.
उत्तर २
A pulse of sound consists of a combination of waves of different wavelength. In a dispersive medium, these waves travel with different velocities giving rise to the distortion in the wave.
संबंधित प्रश्न
When a transverse wave on a string is reflected from the free end, the phase change produced is ..............
(a) zero rad
(b) ` pi/2 ` rad
(c) `(3pi)/4` rad
(d) `pi` rad
A wire of density ‘ρ’ and Young’s modulus ‘Y’ is stretched between two rigid supports separated by a distance ‘L’ under tension ‘T’. Derive an expression for its frequency in fundamental mode. Hence show that `n=1/(2L)sqrt((Yl)/(rhoL))` where symbols have their usual meanings
A transverse harmonic wave on a string is described by y(x, t) = 3.0 sin (36 t + 0.018 x + π/4)
Where x and y are in cm and t in s. The positive direction of x is from left to right.
(a) Is this a travelling wave or a stationary wave?
If it is travelling, what are the speed and direction of its propagation?
(b) What are its amplitude and frequency?
(c) What is the initial phase at the origin?
(d) What is the least distance between two successive crests in the wave?
Explain why (or how): Bats can ascertain distances, directions, nature, and sizes of the obstacles without any “eyes”,
Explain why (or how) Solids can support both longitudinal and transverse waves, but only longitudinal waves can propagate in gases
A transverse wave is produced on a stretched string 0.9 m long and fixed at its ends. Find the speed of the transverse wave, when the string vibrates while emitting the second overtone of frequency 324 Hz.
Explain the reflection of transverse and longitudinal waves from a denser medium and a rared medium.
Longitudinal waves cannot
A wave going in a solid
(a) must be longitudinal
(b) may be longitudinal
(c) must be transverse
(d) may be transverse.
A wave moving in a gas
Figure shows a plot of the transverse displacements of the particles of a string at t = 0 through which a travelling wave is passing in the positive x-direction. The wave speed is 20 cm s−1. Find (a) the amplitude, (b) the wavelength, (c) the wave number and (d) the frequency of the wave.
A steel wire of length 64 cm weighs 5 g. If it is stretched by a force of 8 N, what would be the speed of a transverse wave passing on it?
Consider the following statements about sound passing through a gas.
(A) The pressure of the gas at a point oscillates in time.
(B) The position of a small layer of the gas oscillates in time.
A transverse wave described by \[y = \left( 0 \cdot 02 m \right) \sin \left( 1 \cdot 0 m^{- 1} \right) x + \left( 30 s^{- 1} \right)t\] propagates on a stretched string having a linear mass density of \[1 \cdot 2 \times {10}^{- 4} kg m^{- 1}\] the tension in the string.
Two blocks each having a mass of 3⋅2 kg are connected by a wire CD and the system is suspended from the ceiling by another wire AB (See following figure). The linear mass density of the wire AB is 10 g m−1 and that of CD is 8 g m−1. Find the speed of a transverse wave pulse produced in AB and CD.
An organ pipe, open at both ends, contains
A circular loop of string rotates about its axis on a frictionless horizontal place at a uniform rate so that the tangential speed of any particle of the string is ν. If a small transverse disturbance is produced at a point of the loop, with what speed (relative to the string) will this disturbance travel on the string?
A tuning fork of frequency 440 Hz is attached to a long string of linear mass density 0⋅01 kg m−1 kept under a tension of 49 N. The fork produces transverse waves of amplitude 0⋅50 mm on the string. (a) Find the wave speed and the wavelength of the waves. (b) Find the maximum speed and acceleration of a particle of the string. (c) At what average rate is the tuning fork transmitting energy to the string?
The equation of a standing wave, produced on a string fixed at both ends, is
\[y = \left( 0 \cdot 4 cm \right) \sin \left[ \left( 0 \cdot 314 {cm}^{- 1} \right) x \right] \cos \left[ \left( 600\pi s^{- 1} \right) t \right]\]
What could be the smallest length of the string?
Given below are some functions of x and t to represent the displacement (transverse or longitudinal) of an elastic wave. State which of these represent (i) a traveling wave, (ii) a stationary wave or (iii) none at all:
y = 3 sin (5x – 0.5t) + 4 cos (5x – 0.5t)
