The number of waves counted by an observer on the sea-coast in one minute is 54. If the wavelength of the waves is $5 \text{m}$ then the velocity of the waves in $\text{m/s}$ will be

Question

A transverse wave along a string is given by $ y = 2 \sin \left( 2\pi (3t - x) + \frac{\pi{4} \right) $, where $ x $ and $ y $ are in cm and $ t $ in second. Find the acceleration of a particle located at $ x = 4 $ cm at $ t = 1 $ s.}

Answer 1

Step 1: Distance per minute:
In one minute $54$ wavelengths pass: $54 \times 5 = 270$ m.

Step 2: Speed:
$v = \frac{270\ \text{m}}{60\ \text{s}} = 4.5$ m/s.

Final Answer:
The speed is $4.5$ m/s, option (A). \[ \boxed{4.5\ \text{m/s}} \]

The number of waves counted by an observer on the sea-coast in one minute is 54. If the wavelength of the waves is \(5 \text{m}\) then the velocity of the waves in \(\text{m/s}\) will be

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The Correct Option is A

Solution and Explanation

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