A wave equation is given as $y = \cos (500 t - 70 x)$ , where y is in mm,x in m and t is in sec.

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the wave must be a transverse porpagating wave.

The speed of the wave is 50/7 m/s

The frequency of oscillations $1000 π H z$

Two closest points which are in same phase have separation $20 π / 7 c m .$

answer is B, D.

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Detailed Solution

$y = \cos (500 t - 70 x)$

As $y & x$ both are having units of displacement so it means the wave function is displacement of medium particles and particles of medium are oscillating but it is not mentioned that osicllation of medium particles is in which direction so wave can be transverse or longituadinal.

The wave is propagating along positive X-axis with speed

$V = \frac{50}{7} m / s$ frequency of wave is given by,

$2 π f =: 500 \Rightarrow f = \frac{250}{π} H z$

The seperation between two closest point which are

vibrating in phase are given by, $Δ x = λ = \frac{50 \times π}{7 \times 250} = \frac{π}{35} m = \frac{20 π}{7} c m .$