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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
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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.
A string of mass 2.50 kg is under a tension of 200 N. The length of the stretched string is 20.0 m. If the transverse jerk is struck at one end of the string, how long does the disturbance take to reach the other end?
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) 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 mechanical wave propagates in a medium along the X-axis. The particles of the medium
(a) must move on the X-axis
(b) must move on the Y-axis
(c) may move on the X-axis
(d) may move on the Y-axis.
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.
Two wires of different densities but same area of cross section are soldered together at one end and are stretched to a tension T. The velocity of a transverse wave in the first wire is double of that in the second wire. Find the ratio of the density of the first wire to that of the second wire.
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?
If the speed of a transverse wave on a stretched string of length 1 m is 60 m−1, what is the fundamental frequency of vibration?
A wire, fixed at both ends is seen to vibrate at a resonant frequency of 240 Hz and also at 320 Hz. (a) What could be the maximum value of the fundamental frequency? (b) If transverse waves can travel on this string at a speed of 40 m s−1, what is its length?
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 = 2 cos (3x) sin (10t)
