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1 year ago

The wave function for a traveling wave on a taut string is (in SI units)

Physics

1 answer:

weqwewe [10]1 year ago

5 0

The speed of travel of this wave is 3.333 m/s and the direction of the wave is in the positive direction (+x).
The vertical position of an element of the string at t = 0, x = 0.100 m is equal to 5.5 meters.
The wavelength of this traveling wave is equal to 0.667 meter.
The frequency of this traveling wave is equal to 5 Hertz.
The maximum transverse speed of any element of this string is equal to 11.0 m/s.

<h3>How to determine the speed and direction of travel of the wave? </h3>

Since the wave function for this traveling wave on a taut string is (in SI units) is given by y(x,t) = 0.350sin(10πt - 3πx + π/4). Thus, we can logically deduce that the wavelength and angular wave number are as follows:

Wavelength, ω = 10π rad/s.

Angular wave number, k = 3π rad/m.

Now, we can calculate the speed of travel of this wave:

Speed, v = ω/k

Speed, v = 10π/3π

Speed, v = 3.333 m/s.

Based on the wave function, we can logically deduce that the direction of the wave is in the positive direction (+x).

<h3>How to determine the vertical position of an element of the string?</h3>

The vertical position of an element of the string at t = 0, x = 0.100 m is given by:

y(x, t) = 0.350sin(10πt - 3πx + π/4)

y(0.100, 0) = 0.350sin(10π(0) - 3π(0.100) + π/4)

y(0.100, 0) = 0.350sin(-0.157)

y(0.100, 0) = 0.055 cm × 100 = 5.5 meters.

<h3>How to determine the wavelength?</h3>

Mathematically, the wavelength of a traveling wave is given by this formula:

ω = 2π/k

ω = 2π/3π

Wavelength, ω = 0.667 meter.

<h3>How to determine the frequency?</h3>

Mathematically, the frequency of a traveling wave is given by this formula:

Frequency, f = ω/2π

Frequency, f = 10π/2π

Frequency, f = 5 Hertz.

<h3>What is the maximum transverse speed of an element of this string? </h3>

Mathematically, the maximum transverse speed of any element of this string can be calculated by using this formula:

Vmax = ωA = 2πfA

Vmax = 10 × 3.142 × 0.350

Vmax = 10.997 ≈ 11.0 m/s.

Read more on maximum transverse speed here: brainly.com/question/17485563

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Complete Question:

The wave function for a traveling wave on a taut string is (in SI units).

(a) What are the speed and direction of travel of the wave?

(b) What is the vertical position of an element of the string at t = 0, x = 0.100 m?

What are (c) the wavelength and (d) the frequency of the wave?

(e) What is the maximum transverse speed of an element of the string?

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