A string fixed at both ends is vibrating in its third harmonic. The equation for its vibration is given by y = (0.4 cm) [(0.314 cm^ -1 ) x] [(600π s^ -1 )t] . Determine the wavelength and the speed of the two travelling

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Correct answer: C. 20 cm and 60 m/s

The given equation of the standing wave is

y = 0.4 \sin(0.314 x) \cos(600\pi t)

.

Comparing this with the standard equation of a standing wave

y = 2A \sin(kx) \cos(\omega t)

, we get:

k = 0.314 \text{ cm}^{-1}

\omega = 600\pi \text{ s}^{-1}

The wavelength

\lambda

is given by:

\lambda = \dfrac{2\pi}{k} = \dfrac{2 \times 3.14}{0.314} = 20 \text{ cm}

The speed

v

of the travelling waves is given by:

v = \dfrac{\omega}{k} = \dfrac{600\pi}{0.314} = \dfrac{600 \times 3.14}{0.314} = 6000 \text{ cm/s} = 60 \text{ m/s}

A string fixed at both ends is vibrating in its third harmonic. The...

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