Complete these two projects.

You will need the following items: a rope about 10 to 20 meters long, a meter or yard stick, a watch that records seconds, and a helper. Tie one end of the rope to a doorknob or other secure object at about waist height. Have your helper take one end of the rope and whip it up and down, while you watch. Answer the questions below.

What type of wave was created? How do you know?

Estimate the wavelength of the wave produced.

Estimate the frequency of the wave produced. This is most easily estimated by counting the number of waves that pass the measuring device within a particular time interval as measured on your watch, or by counting the number of times the hand is shaken up and down.

Compute the velocity of your wave.

Lay a slinky on a table and secure one end to one edge of the table. Stretch the slinky across the length of the table and give the free end a quick push in the direction of the secured end. Answer the questions below.

A slinky photograph
What type of wave was created? How do you know?

Estimate the wavelength of the wave produced.

Estimate the frequency of the wave produced. This is most easily estimated by counting the number of waves that pass the measuring device within a particular time interval as measured on your watch, or by counting the number of times the hand is shaken up and down.

Compute the velocity of your wave.

1 answer

Sure! I can guide you through both projects and help you understand the concepts involved.

Project 1: Rope Wave Experiment

  1. What type of wave was created? How do you know?

    • The wave created in this experiment is a transverse wave. You can identify it as a transverse wave because the motion of the rope (up and down) is perpendicular to the direction in which the wave travels (along the length of the rope).
  2. Estimate the wavelength of the wave produced.

    • To estimate the wavelength (λ), measure the distance from one peak of the wave to the next peak using a meter stick. For a practical estimation, it could be around 1 to 2 meters depending on how vigorously your helper whipped the rope.
  3. Estimate the frequency of the wave produced.

    • Count the number of complete waves (one full cycle from crest to crest or trough to trough) that pass a fixed point (like your helper's position) in a given timeframe (e.g., 10 seconds). Divide the number of waves counted by the number of seconds to find the frequency (f). For example, if you counted 5 waves in 10 seconds, the frequency would be \( f = \frac{5 \text{ waves}}{10 \text{ seconds}} = 0.5 \text{ Hz} \).
  4. Compute the velocity of your wave.

    • The wave velocity (v) can be calculated using the formula: \[ v = f \cdot \lambda \] If you estimated the wavelength to be 2 meters and the frequency to be 0.5 Hz, then: \[ v = 0.5 , \text{Hz} \times 2 , \text{m} = 1 , \text{m/s} \]

Project 2: Slinky Wave Experiment

  1. What type of wave was created? How do you know?

    • The wave created in the slinky experiment is a longitudinal wave. This is evident because the motion of the slinky (the compression and rarefaction of the coils) is parallel to the direction in which the wave travels.
  2. Estimate the wavelength of the wave produced.

    • To estimate the wavelength, measure the distance between two consecutive compressions (or rarefactions) in the slinky. This distance can vary, but it may be around 0.5 to 1 meter based on how you pushed the slinky.
  3. Estimate the frequency of the wave produced.

    • Similar to the first experiment, count the number of waves that pass by a fixed point in a set timeframe (e.g., in 10 seconds). If you counted 6 compressions in that time, the frequency would be \( f = \frac{6 \text{ waves}}{10 \text{ seconds}} = 0.6 , \text{Hz} \).
  4. Compute the velocity of your wave.

    • Using the same formula as in the first experiment: \[ v = f \cdot \lambda \] If the wavelength is estimated to be 0.5 meters and the frequency is 0.6 Hz: \[ v = 0.6 , \text{Hz} \times 0.5 , \text{m} = 0.3 , \text{m/s} \]

Conclusion

Through these projects, you've explored two types of waves: transverse waves created with the rope and longitudinal waves created with the slinky. You have estimated the wavelength, frequency, and computed the velocity for both types of waves. Make sure to record your results and observations for further analysis!