Write a wave function describing the wave

y = 0.075 cos (1.05 x - 4 π t)

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y = 0.075 cos (1.05 x - 2 t)

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y = 0.075 sin (1.05 x - 4 π t)

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Solution

The correct option is B $y = 0.075 cos (1.05 x - 4 π t)$
Given that, the amplitude is maximum at the end at t = 0. This makes the wave a cos function. From the given data,
frequency f = 2Hz
wave speed V = 12 m/s
Amplitude A = 0.075 m
The standard cos wave function is given by y = A cos(kx - $Ω$ t),
where,
$Ω$ = Angular frequency = kV
k = wave number = 2 $π$ / wavelength( $λ$ )
\lambda = V/f = 6 m
$k = 2 π / 6 = 1.05 1 / m$
$Ω$ = kV = 12* $π$ / 3 = 4 $π$
From these values, substituting in the standard equation, we have
y = 0.075 cos (1.05x - 4 $π$ t)

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