Question

A transverse mechanical wave is traveling along a string lying along the x-axis. The displacement of the string as a function of position and time, y(x,t), is described by the following equation:
$y(x,t)=0.0480$×$sin(5.40x-128t)$
where x and y are in meters and the time is in seconds.
1. What is the wavelength of the wave?
2. What is the velocity of the wave? (Define positive velocity along the positive x-axis.)
3. What is the maximum speed in the y-direction of any piece of the string? (Give a positive answer for speed.)

Answer 1

(1) The wavelength of the wave is 1.164 m.

(2) The  velocity of the wave is 23.7 m/s.

(3) The maximum speed in the y-direction of any piece of the string is 6.14 m/s.

Wavelength of the wave

A general wave equation is given as;

y(x, t) = A sin(Kx - ωt)

Velocity of the wave

v = ω/K

From the given wave equation, we have,

y(x, t) = 0.048 sin(5.4x - 128t)

v = ω/K

where;

• ω corresponds to 128
• k corresponds to 5.4

v = 128/5.4

v = 23.7 m/s

Wavelength of the wave

λ = 2π/K

λ = (2π)/(5.4)

λ = 1.164 m

Maximum speed of the wave

v(max) = Aω

where;

• A is amplitude of the wave
• ω is angular speed of the wave

v(max) = (0.048)(128)

v(max) = 6.14 m/s

Thus, the wavelength of the wave is 1.164 m.

The  velocity of the wave is 23.7 m/s.

The maximum speed in the y-direction of any piece of the string is 6.14 m/s.

Learn more about wavelength here: brainly.com/question/10728818

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