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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: - CBSE (Science) Class 11 - Physics

ConceptReflection of Transverse and Longitudinal Waves

Question

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

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.

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Solution 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: Concept: Reflection of Transverse and Longitudinal Waves.
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