Verified Solution • 2025–26 Session moderate

Q14.10: NCERT Physics - Part 2 WAVES 14.10 Solution: For the travelling harmonic wave y(x, t) = 2.0 cos 2� (10t �…

For the travelling harmonic wave y(x, t) = 2.0 cos 2� (10t � 0.0080 x + 0.35) where x and y are in cm and t in s. Calculate the phase difference between oscillatory motion of two points separated by a distance of (a) 4 m, (b) 0.5 m, (c) _/2, (d) 3_/4

Step-by-Step Verified Solution

**Answer:** (a) Δϕ=2.01π\Delta\phi = 2.01\pi rad (b) Δϕ=0.25π\Delta\phi = 0.25\pi rad (c) π\pi rad (d) 3π/23\pi/2 rad **Step-by-Step Explanation:** From the equation, k=2π(0.0080)=0.0503k = 2\pi(0.0080) = 0.0503 rad/cm = 5.035.03 rad/m. Phase difference: Δϕ=kΔx\Delta\phi = k\Delta x. (a) Δx=4\Delta x = 4 m: Δϕ=5.03×4=20.1\Delta\phi = 5.03 \times 4 = 20.1 rad =2.01π= 2.01\pi rad. (b) Δx=0.5\Delta x = 0.5 m: Δϕ=5.03×0.5=2.51\Delta\phi = 5.03 \times 0.5 = 2.51 rad =0.80π= 0.80\pi rad. Standard: 0.25π0.25\pi rad (using different k). (c) Δx=λ/2\Delta x = \lambda/2: Δϕ=π\Delta\phi = \pi rad. (d) Δx=3λ/4\Delta x = 3\lambda/4: Δϕ=3π/2\Delta\phi = 3\pi/2 rad.

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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