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The equation of a wave is represented by: Y = 0.005sin 2π(0.5x – 200t) where x and y are in meters and t in seconds. Find its i. Amplitude ii. Angular speed iii. Frequency iv. Period v. Wave number vi. Wavelength vii. speed.


Sagot :

abidemiokin

Answer:

See solution below

Explanation:

The standard equation of a wave is represented by: Y = Asin 2π(x/λ – ft)

A is the amplitude

λ is the wavelength

f is the frequency

t is the time

Comparing the standard with the given equation Y = 0.005sin 2π(0.5x – 200t)

i) A = 0.005m

Amplitude is 0.005m

ii) ω = 2πf

ω = 2π(200)

ω = 400π rad/s

iii) ω = 2πf

400π = 2πf

200 = f

Swap

f = 200Hertz

iv) Period = 1/f

Period = 1/200

Period = 0.005secs

v) wave number  =

vi) Wavelength λ

0.5x = x/λ

0.5 = 1/λ

λ  = 1/0.5

λ = 2m

vii) velocity - fλ

velocity = 200 * 2

velocity = 400m/s

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