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Speed in a Medium

The mathemati...

Question

The mathematical form of three travelling waves are given by
$Y_{1} = (2 c m) s i n (3 x - 6 t) Y_{2} = (3 c m) s i n (4 x - 12 t) a n d Y_{3} = (4 c m) s i n (5 x - 11 t)$
of these waves,

A

Wave 1 has greatest wave speed and greatest maximum transverse string speed

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B

Wave 2 has greatest wave speed and wave 1 has greatest maximum transverse string speed

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C

Wave 3 has greatest wave speed and wave 1 has greatest maximum transverse string speed

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D

Wave 2 has greatest wave speed and wave 3 has greatest maximum transverse string speed.

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Solution

The correct option is D Wave 2 has greatest wave speed and wave 3 has greatest maximum transverse string speed.
For the wave, $y = A s i n (k x - ω t)$ , the wave speed is $\frac{ω}{k}$ and the maximum transvers string speed is $A ω$

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