Verified Solution • 2025–26 Session moderate

Q14.13: NCERT Physics - Part 2 WAVES 14.13 Solution: Given below are some functions of x and t to represent the…

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 travelling wave, (ii) a stationary wave or (iii) none at all: (a) y = 2 cos (3x) sin (10t) (b) y = 2�(x � vt) (c) y = 3 sin (5x � 0.5t) + 4 cos (5x � 0.5t) (d) y = cos x sin t + cos 2x sin 2t

Step-by-Step Verified Solution

**Answer:** (a) Stationary wave (b) None (c) Travelling wave (d) Stationary wave **Step-by-Step Explanation:** (a) The terms

\cos(3x)

and

\sin(10t)

appear separately, so it represents a stationary wave . (b)

y = 2\sqrt{x-vt}

is not a harmonic function and does not represent a wave . (c) The terms

(5x - 0.5t)

appear in the combination

kx - \omega t

, so it represents a travelling wave [citation:2]. (d) The terms

x

and

t

appear separately, so it represents a stationary wave (superposition of two stationary waves) [citation:2].

All Questions in this Chapter

Q14.1 Q14.2 Q14.3 Q14.4 Q14.5 Q14.6 Q14.7 Q14.8 Q14.9 Q14.10 Q14.11 Q14.12 Q14.13 Q14.14 Q14.15 Q14.16 Q14.17 Q14.18 Q14.19

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