A string oscillates according to the equation $y^{'} = (0.50 c m) sin [(\frac{π}{3} c m^{- 1}) x] cos [(40 π s^{- 1}) t]$ . What is the speed of the two waves(identical except for direction of travel) whose superposition gives this oscillation?

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Solution

We know that $v = \frac{ω}{k}$

Here $ω = 40 π / s$ and $k = \frac{π}{3} / c m$

$⟹ v = \frac{40 π}{π / 3} = 120 c m / s$

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A string oscillates according to the equation y′=(0.50cm)sin[(π3cm−1)x]cos[(40πs−1)t]. What is the speed of the two waves(identical except for direction of travel) whose superposition gives this oscillation?

We know that v=ωkHere ω=40π/s and k=π3/cm⟹v=40ππ/3=120cm/s

A string oscillates according to the equation $y^{'} = (0.50 c m) sin [(\frac{π}{3} c m^{- 1}) x] cos [(40 π s^{- 1}) t]$ . What is the speed of the two waves(identical except for direction of travel) whose superposition gives this oscillation?

We know that $v = \frac{ω}{k}$

Here $ω = 40 π / s$ and $k = \frac{π}{3} / c m$

$⟹ v = \frac{40 π}{π / 3} = 120 c m / s$