Suppose you observed the equation for a traveling wave to be y(x, t) = A cos(kx − ????t), where its amplitude of oscillations was 0.15 m, it

Question

Suppose you observed the equation for a traveling wave to be y(x, t) = A cos(kx − ????t), where its amplitude of oscillations was 0.15 m, its wavelength was two meters, and the period was 2/15 s. If a point on the wave at a specific time has a displacement of 0.12 m, what is the transverse speed of that point?

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Linh Đan 6 months 2021-08-10T15:27:02+00:00 1 Answers 2 views 0

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    2021-08-10T15:28:26+00:00

    Answer:

    15m/s

    Explanation:

    The equation for a traveling wave as expressed as y(x, t) = A cos(kx − \omegat) where An is the amplitude f oscillation, \omega is the angular velocity and x is the horizontal displacement and y is the vertical displacement.

    From the formula; k =\frac{2\pi x}{\lambda} \ and \ \omega = 2 \pi f where;

    \lambda \ is\ the \ wavelength \ and\ f \ is\ the\ frequency

    Before we can get the transverse speed, we need to get the frequency and the wavelength.

    frequency = 1/period

    Given period = 2/15 s

    Frequency = \frac{1}{(2/15)}

    frequency = 1 * 15/2

    frequency f = 15/2 Hertz

    Given wavelength \lambda = 2m

    Transverse speed v = f \lambda

    v = 15/2 * 2\\\\v = 30/2\\\\v = 15m/s

    Hence, the transverse speed at that point is  15m/s

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