MHT CET · Physics · Waves and Sound

A progressive wave is represented by $y = 12 \sin (5 t - 4 x)$ $cm$ . On this wave, how far away are the two points having a phase difference of $90 °$ ?

A $\frac{π}{2} c m$
B $\frac{π}{4} c m$
C $\frac{π}{8} c m$
D $\frac{π}{16} c m$

Verified Solution

Answer & Solution

Correct Answer

(C) $\frac{π}{8} c m$

Step-by-step Solution

Detailed explanation

y = 12 \sin (5 t - 4 x)

Comparing in

y = A \sin (w t - k x)

We have

A = 12, w = 5 a n d k = 4

(w t - k x) =

phase difference

= \frac{π}{2}

∴ | 5 t - 4 x | = \frac{π}{2}

When

t = 0, 4 x = \frac{π}{2}

∴ x = \frac{π}{8} c m

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 progressive wave is represented by y=12sin⁡(5t-4x) cm. On this wave, how far away are the two points having a phase difference of 90°?

Step-by-step Solution

A progressive wave is represented by $y = 12 \sin (5 t - 4 x)$ $cm$ . On this wave, how far away are the two points having a phase difference of $90 °$ ?