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The wavefunction of a harmonic wave on a string is y(x,t) = 0.004 sin(44.5x + 237.0t), where x and y are in m and t is in s. What is the speed of the wave taking positive to be in the +x direction and negative to be in the -x direction.

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Final answer:

The speed of the wave is 5.34 m/s.

Step-by-step explanation:

The wavefunction given is y(x,t) = 0.004 sin(44.5x + 237.0t).

To find the speed of the wave, we need to determine the wave speed. The wave speed is given by the formula v = λf, where λ is the wavelength and f is the frequency.

From the wavefunction, the wavelength can be found as λ = 2π/k, where k is the wave number. Comparing this with the given expression, we have k = 44.5m⁻¹.

The frequency can be found from the angular frequency using the formula f = ω/2π, where ω is the angular frequency. Comparing this with the given expression, we have ω = 237.0s⁻¹.

Substituting these values into the formula v = λf, we have v = (2π/k)(ω/2π) = ω/k = (237.0s⁻¹)/(44.5m⁻¹) = 5.34m/s.

User Buwaneka Sudheera
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