Question 2 of 23intermediate🔧 ApplyNumerical3 marks

For the travelling harmonic wave y(x,t)=2.0cos⁡2π(10t−0.0080x+0.35)y(x, t) = 2.0 \cos 2\pi (10t - 0.0080 x + 0.35) where xx and yy are in cm and tt in s. Calculate the phase difference between oscillatory motion of two points separated by a distance of

(a)

4 m

Answer

6.4π rad

(b)

0.5 m

Answer

0.8π rad

(c)

λ/2\lambda/2

Answer

π rad

(d)

3λ/43\lambda/4

Answer

3π/2 rad

Explanation

This question tests understanding of phase difference in travelling waves. The phase difference between two points separated by distance Δx is directly proportional to the wave number k. From the given wave equation, we extract k and use the relation Δφ = k·Δx. For distances expressed in terms of wavelength, we use the fundamental relation that separation of λ corresponds to phase difference of 2π.

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