Calculating Phase Angle and Amplitude for a Sinusoidal Wave on a String

In summary, the problem involves a sinusoidal wave with a frequency of 230 Hz and an amplitude of +4.8 mm. The smallest positive phase angle is found to be 1.678 radians. It is noted that the answer for part B is correct, but the answer for part C is incorrect due to a negative value for the angular frequency. The correct solution for part C is found to be t = 0.0011 seconds.
  • #1
armolinasf
196
0

Homework Statement



At time t = 0 and at position x = 0 m along a string, a rightward (+x dir) traveling sinusoidal wave with frequency of 230 Hz has displacement y = +4.8 mm and transverse velocity vy = -0.75 m/s.

What is the smallest positive phase angle?

What is the amplitude of the wave?

How long does an observer at x=0 need to wait before a trough (y=-A) arrives?





The Attempt at a Solution



.0048=Asin(phi)
-.75=acos(phi)

arctan[2(pi)(230)(.0048/-.75)]=phi=-1.463

pi-1.463=1.678rad

For some reason this answer is incorrect and I don't know why since I used in my calculation of part B which is correct.

B) .0048/sin(1.678)=.00483m

Not sure how to approach part c...

As always thanks for the help
 
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  • #2
for c I would just solve t for -A correct, omega would be negative since the wave is moving rightward?

arcsin(-1)/(-2pi*230)=t=.0011

Does this make sense?
 

FAQ: Calculating Phase Angle and Amplitude for a Sinusoidal Wave on a String

What is the phase angle for a wave equation?

The phase angle for a wave equation is the angle in radians that represents the displacement of a wave at a given point in time. It is used to measure the position of a wave within one complete cycle, and can be calculated by dividing the displacement by the wavelength and multiplying by 2π.

How is phase angle related to frequency and wavelength?

Phase angle is directly related to frequency and wavelength. As the frequency increases, the phase angle also increases. This means that the position of the wave at a given point in time is changing more rapidly. Similarly, as the wavelength increases, the phase angle also increases, indicating a slower change in position of the wave.

Why is phase angle important in wave equations?

Phase angle is important in wave equations because it allows us to track the position of a wave at a specific point in time. By knowing the phase angle, we can determine the displacement and direction of the wave at any given time, and use this information to understand and predict the behavior of waves.

How is phase angle represented graphically?

Phase angle can be represented on a graph by plotting the displacement of the wave at different points in time. The phase angle can then be calculated by finding the angle between the displacement and the x-axis at a particular point in time. This can be visualized as the position of a point on the unit circle in trigonometry.

How is phase angle used in practical applications?

Phase angle is used in a variety of practical applications, such as in the study of sound and light waves, as well as in electronic circuit design. It is also important in fields such as seismology and telecommunications, where accurate measurements of wave behavior are essential for understanding and predicting events.

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