- The frequency and angular frequency are 0.500 Hertz and 3.142 rad/s. respectively.
- The angular wave number is equal to 3.142 rad/m.
- The wave function for this wave is given by: y = Asin(kx - ωt + Φ).
- The equation of motion for the left end of the string is given by: y = 0.100sin(3.142x - 3.142t + 0).
- The equation of motion for the left end of the string at x = 1.50 m to the right is equal to y = 0.100sin(4.71 - 3.142t + 0).The maximum speed of any point on the string is 0.3142 m/s.
<h3>How to calculate the frequency and angular frequency?</h3>
First of all, we would determine the frequency of this wave by using this formula:
Frequency = wavelength/speed
Frequency = 0.100/2.00
Frequency = 0.500 Hertz.
For the angular frequency, we have:
Angular frequency, ω = 2πf
Angular frequency, ω = 2 × 3.142 × 0.500
Angular frequency, ω = 3.142 rad/s.
<h3>How to determine the angular wave number?</h3>
Angular wave number, k = 2π/∧
Angular wave number, k = (2 × 3.142)/2.00
Angular wave number, k = 3.142 rad/m.
<h3>How to determine the wave function for this wave?</h3>
Mathematically, the wave function for this wave is given by:
y = Asin(kx - ωt + Φ)
For the equation of motion for the left end of the string, we have:
y = 0.100sin(3.142x - 3.142t + 0)
For the equation of motion for the left end of the string at x = 1.50 m to the right, we have:
y = 0.100sin(3.142x - 3.142t + 0)
y = 0.100sin(3.142(1.5) - 3.142t + 0)
y = 0.100sin(4.71 - 3.142t + 0)
<h3>What is the maximum speed of any point on the string?</h3>
Vy = 0.100sin(- 3.142)cos(3.142x - 3.142t)
Vy ≤ 0.3142 m/s (since cosine varies +1 and -1).
Read more on wave function here: brainly.com/question/11181093
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Complete Question:
A sinusoidal wave of wavelength 2.00 m and amplitude 0.100 m travels on a string with a speed of 1.00 m/s to the right. Initially, the left end of the string is at the origin. Find:
(a) the frequency and angular frequency,
(b) the angular wave number, and
(c) the wave function for this wave.
Determine the equation of motion in SI units for
(d) the left end of the string, and
(e) the point on the string at x = 1.50 m to the right of the left end.
(f) What is the maximum speed of any point on the string?
