MHT CET · Physics · Waves and Sound

A simple harmonic progressive wave is represented as y = 0.03 $s i n π (2 t - 0.01 x) m$ . At a given instant of time, the phase difference between two particles 25 m apart is

A $π r a d$
B $\frac{π}{2} r a d$
C $\frac{π}{4} r a d$
D $\frac{π}{8} r a d$

Verified Solution

Answer & Solution

Correct Answer

(C) $\frac{π}{4} r a d$

Step-by-step Solution

Detailed explanation

The given equation of SHM wave is

y = 0.03 s i n π (2 t - 0.01 x) m

0.03 \sin (2 π t - 0.01 π x) m

Comparing it with general equation, we get

y = asin (ω t - k x)

Where,

k = \frac{2 π}{λ} \Rightarrow λ = 200 m

The phase difference between two particles is given by

Δ ϕ = k x = \frac{2 π}{λ} \times x

… (i)
Here, x = 25 m
Substituting the values of x an

λ

in Eq. (i), we get

Δ ϕ = \frac{2 π}{200} \times 25 = \frac{π}{4} r a d

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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A simple harmonic progressive wave is represented as y = 0.03 sinπ2t-0.01xm . At a given instant of time, the phase difference between two particles 25 m apart is

Step-by-step Solution

A simple harmonic progressive wave is represented as y = 0.03 $s i n π (2 t - 0.01 x) m$ . At a given instant of time, the phase difference between two particles 25 m apart is