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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: - Physics

Given below are some functions of and 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:

(a) = 2 cos (3x) sin (10t)

(b) `y = 2sqrt(x- vt)`

(c) = 3 sin (5– 0.5t) + 4 cos (5– 0.5t)

(d) = cos sin + cos 2sin 2t

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Solution 1

(a) The given equation represents a stationary wave because the harmonic terms kxand ωt appear separately in the equation.

(b) The given equation does not contain any harmonic term. Therefore, it does not represent either a travelling wave or a stationary wave.

(c) The given equation represents a travelling wave as the harmonic terms kx and ωtare in the combination of kx – ωt.

(d) 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.

Solution 2

(a) It represents a stationary wave.

(b) It does not represent either a travelling wave or a stationary wave.

(c) It is a representation for the travelling wave.

(d) It is a superposition of two stationary wave.

  Is there an error in this question or solution?
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APPEARS IN

NCERT Class 11 Physics Textbook
Chapter 15 Waves
Q 13 | Page 388
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