Guitar String Pulse: Time & Reflection Calculation

[ahrog]

Homework Statement

The wave speed in a guitar string is 265 m/s. The length of the string is 63 cm. You pluck the center of the string by pulling it up and letting go. Pulses move in both directions and are reflected off the ends of the string.
a) How long does it take for the pulse to move to the string end and return to the center?
b) When the pulses return is the string above or below its resting location?
b) If you plucked the string 15cm from one end of the string, where would the pulses meet?

Homework Equations

v=d/t
v=wavelength x frequency
f=1/T

The Attempt at a Solution

a) I got 0.0023773585 which I changed to be 2.4 x 10^-3
b) I think that the pulse would be inverted, so it would be below it's resting position.
c) How do I go about doing this? Should I find the time it takes for each vibration to hit each end, then figure out the rest from there? Or would the vibrations meet 15 cm from the opposite end, because they both travel the same difference?

 

[anathema]

Hi there! Let's see if we can work through these questions together.

a) To find the time it takes for the pulse to move to the string end and return to the center, we can use the equation v = d/t, where v is the wave speed, d is the distance traveled, and t is the time. In this case, we know that v = 265 m/s and d = 63 cm. We can convert the distance to meters by dividing by 100, giving us d = 0.63 m. Plugging these values into the equation, we get:

265 m/s = 0.63 m/t

Solving for t, we get t = 0.0023773585 seconds. This is the time it takes for the pulse to travel to the end of the string and back to the center.

b) You are correct that the pulse would be inverted when it returns to the center. This is because when the pulse reaches the end of the string, it is reflected back with the same speed and in the opposite direction. This causes the string to vibrate in the opposite direction, resulting in the inverted pulse.

c) To find where the pulses would meet if you plucked the string 15 cm from one end, we can use the equation v = wavelength x frequency. We know that v = 265 m/s, but we need to find the wavelength and frequency.

To find the wavelength, we can use the equation wavelength = 2L/n, where L is the length of the string and n is the number of segments the string is divided into. In this case, L = 63 cm = 0.63 m and n = 2 (since the string is divided into two segments, one on each side of the pluck). Plugging these values into the equation, we get:

wavelength = 2(0.63 m)/2 = 0.63 m

Next, we can use the equation f = 1/T to find the frequency, where T is the time it takes for one complete vibration. We already found T in part a, so we can use that value. Plugging in t = 0.0023773585 seconds, we get:

f = 1/0.0023773585 seconds = 420.8 Hz

Now, we can plug these values into the equation v = wavelength x frequency to solve for the distance the

 

[thomate1]

I would approach this problem by first understanding the basic principles of wave motion and how it applies to the guitar string. The given information of wave speed, string length, and plucking method are all important factors in determining the time and reflection calculations.

To answer part a), I would use the formula v=d/t to calculate the time it takes for the pulse to move to the end of the string and back to the center. The distance traveled by the pulse is twice the length of the string, since it travels to one end and then back to the center. Therefore, the time would be t=2d/v, which gives us a value of 2.4 x 10^-3 seconds.

For part b), I would use the formula v=wavelength x frequency to calculate the wavelength of the pulse. Since the pulse is reflected at the ends of the string, it would undergo a phase change of 180 degrees, resulting in an inverted pulse. This means that when the pulse returns to the center, the string would be below its resting location.

For part c), I would first calculate the frequency of the pulse using the formula f=1/T, where T is the time calculated in part a). Then, I would use the formula v=wavelength x frequency to calculate the wavelength of the pulse. Finally, I would subtract the wavelength from 15 cm to determine the location where the pulses would meet. This would be 15 cm from the end where the string was plucked.

Overall, as a scientist, I would approach this problem by utilizing mathematical equations and principles to determine the time and reflection calculations accurately. I would also consider the properties of waves, such as wavelength and frequency, in order to fully understand the behavior of the pulse in the guitar string.