Oscillating String - Transverse Speed, what am I doing wrong?

In summary: You are an amazing summarizer!In summary, the given equation describes a string oscillation with a amplitude of 0.654 cm and a speed of 24.2π s-1. The distance between nodes is not specified. To find the transverse speed of a particle at a specific position and time, we use the equation u = ∂y´/∂t = (0.654 cm) (24.2π s-1) sin[(π/4.0 cm-1)x] (-1) sin[(24.2π s-1)t]. Plugging in x = 1.24 cm and t = 1.13 s, we get a transverse speed of -36.
  • #1
Malavin
4
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A string oscillates according to the equation
y´ = (0.654 cm) sin[(π/4.0 cm-1)x] cos[(24.2π s-1)t].
What are the (a) amplitude and (b) speed of the two waves (identical except for direction of travel) whose superposition gives this oscillation? (c) What is the distance between nodes? (d) What is the transverse speed of a particle of the string at the position x = 1.24 cm when t = 1.13 s?
Give your answers in centimeter-based units.

I only need help with part d, the other parts I have gotten right.
Here's my attempt at solving:

u = ∂y´/∂t = (0.654 cm) (24.2π s-1) sin[(π/4.0 cm-1)x] (-1) sin[(24.2π s-1)t]

Then, plugging in x and t:

u = (-0.654 cm) (24.2π s-1) sin[(π/4.0 cm-1)(1.24 cm)] sin[(24.2π s-1)(1.13 s)]

u = -32.9 cm/s

When I plug this solution in, I am told that it is not the correct answer. Even when I tried neglecting the negative sign. I am not sure how my calculations are wrong, but I would love to be enlightened!
 
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  • #2
Your method looks fine. I get a different number. Are you sure your calculator is in radian mode?
 
  • #3
Oops! I looked at the equation again and it's π/4.0 cm-1, not 4.0π. That is what I used to get the result I did. I have gone back and edited my original post to reflect this. I hope that when calculated with π/4, you get the same thing as I do.

EDIT: Okay, apparently my method was right, but there is something wrong with my calculator. Just plugged in the numbers to Wolfram and received 36.4 cm/s which is the right answer.

Final Edit: Yes, I must have been using parentheses dumb or something. Just plugged it into my calculator again and got 36.4 cm/s. I feel dumb now, but I got the right answer after all! :)

Thank you for your help!
 
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FAQ: Oscillating String - Transverse Speed, what am I doing wrong?

Why is my oscillating string not moving as fast as I expect?

There could be several reasons for this. One possible reason is that the tension in the string is not high enough, which affects the speed of the oscillation. Another reason could be friction or resistance in the medium the string is moving through. Additionally, the frequency and amplitude of the oscillation also play a role in determining the speed.

Can the transverse speed of an oscillating string be greater than the speed of sound?

No, the transverse speed of an oscillating string cannot be greater than the speed of sound. The speed of sound is the maximum speed at which a disturbance can travel through a medium, and the string is limited by this speed. However, the transverse speed of an oscillating string can approach the speed of sound depending on the tension, frequency, and amplitude of the oscillation.

How does the length of the string affect its transverse speed?

The length of the string does not directly affect its transverse speed. The speed of an oscillating string is primarily influenced by the tension, frequency, and amplitude. However, if the length of the string is changed, the tension and frequency may also change, which can ultimately affect the speed of the oscillation.

What is the relationship between transverse speed and wavelength in an oscillating string?

The transverse speed of an oscillating string is directly proportional to the wavelength of the oscillation. This means that as the transverse speed increases, the wavelength also increases, and vice versa. This relationship is described by the equation v = fλ, where v is the transverse speed, f is the frequency, and λ is the wavelength.

Can I change the transverse speed of an oscillating string by adjusting the tension?

Yes, the transverse speed of an oscillating string can be changed by adjusting the tension. As the tension increases, so does the speed of the oscillation. This is because a higher tension creates a higher restoring force, allowing the string to move faster. However, there are other factors, such as frequency and amplitude, that also affect the transverse speed and must be taken into account when adjusting tension.

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