Advertisements
Advertisements
प्रश्न
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 = cos x sin t + cos 2x sin 2t
Advertisements
उत्तर
The given equation represents a stationary wave because the harmonic terms kxand ωt appear separately in the equation. This equation actually represents the superposition of two stationary waves.
संबंधित प्रश्न
When longitudinal wave is incident at the boundary of denser medium, then............................
- compression reflects as a compression.
- compression reflects as a rarefaction.
- rarefaction reflects as a compression.
- longitudinal wave reflects as transverse wave.
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) The shape of a pulse gets distorted during propagation in a dispersive medium.
You are walking along a seashore and a mild wind is blowing. Is the motion of air a wave motion?
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
A particle on a stretched string supporting a travelling wave, takes 5⋅0 ms to move from its mean position to the extreme position. The distance between two consecutive particles, which are at their mean positions, is 2⋅0 cm. Find the frequency, the wavelength and the wave speed.
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.
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.
In the arrangement shown in figure , the string has a mass of 4⋅5 g. How much time will it take for a transverse disturbance produced at the floor to reach the pulley? Take g = 10 m s−2.
A steel wire of mass 4⋅0 g and length 80 cm is fixed at the two ends. The tension in the wire is 50 N. Find the frequency and wavelength of the fourth harmonic of the fundamental.
Three resonant frequencies of a string are 90, 150 and 210 Hz. (a) Find the highest possible fundamental frequency of vibration of this string. (b) Which harmonics of the fundamental are the given frequencies? (c) Which overtones are these frequencies? (d) If the length of the string is 80 cm, what would be the speed of a transverse wave on this 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" = 2sqrt(x - "vt")`
