Question

The equation of a plane progressive wave is given by y = 5 cos (200t - x/150) where x and y are in cm and t is in second. The velocity of the wave is
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Answer 1

Given :-

y = 5 cosπ(200t - x/150)

y = 5 cos(200πt -πx/150)

Comparing this equation to the standard equation we get,

w = 200π , k = π/150

2πf = 200π , 2π/λ = π/150

f = 100 Hz , λ = 300 cm = 300/100 = 3 m

v = fλ

v = 100 × 3

v = 300 ms-¹

Hence,

The velocity = v = 300 ms-¹

Answer 2

Given:

• The equation of a plane progressive wave is:

$y = 5 \cos(200t - \dfrac{x}{150} )$

To find:

• Velocity of wave ?

Calculation:

The velocity of wave of a plane progressive wave equation can be calculated in the following method.

$\rm \: v = f \times \lambda$

$\rm \implies \: v = \dfrac{f}{ \dfrac{1}{ \lambda} }$

• Multiplying numerator and denominator with 2π:

$\rm \implies \: v = \dfrac{2\pi f}{ \dfrac{2\pi}{ \lambda} }$

• 2πf is written as $\omega$ and $2\pi/\lambda$ is written as k.

$\rm \implies \: v = \dfrac{ \omega}{ k}$

$\rm \implies \: v = \dfrac{ 200}{ \dfrac{1}{150} }$

$\rm \implies \: v =30000 \: cm/s$

$\rm \implies \: v =300 \: m/s$

So, velocity of wave is 300 m/s