Transverse waves on a string have wave speed $12.0$ m/s, amplitude $0.05 m$ and wavelength $0.4 m$ . The waves travel in the $+ x$ direction and at $t = 0$ , the $x = 0$ end of the string has zero displacement and is moving upwards. Write a wave function describing the wave.

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Solution

A wave traveling in +x direction is represented by $y = A s i n (ω t - k x)$
where $ω = 2 π ν$
and $k = \frac{2 π}{λ}$
We know that speed of wave= $v = λ ν$
Thus here
$ω = 2 π \times \frac{v}{λ} = 2 π \times \frac{12}{0.4} = 60 π s^{- 1}$
and $k = \frac{2 π}{0.4} = 5 π m^{- 1}$
Thus wave is $y = (0.05 m) s i n ((60 π s^{- 1}) t - (5 π m^{- 1}) x)$

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