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The Skewer Wave Machine: Wavelength, Swing and Energy

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The Skewer Wave Machine: Wavelength, Swing and Energy

Use data from a homemade wave machine to connect amplitude, energy and wavelength.

Part 1: Frequency, wavelength and speed

Read the build notes and Table 1, then answer the questions.

Build Notes: A Wave You Can Watch

1Every Tuesday evening, the Riverside Commons Makerspace opens its workbenches to teens. This month, eighth graders Anselm Brandvold and Noemi Achike are building a wave machine for the town's children's museum, with help from their mentor, Mr. Thaddeus Lorne. The machine is simple: a strip of wide tape 2.0 m long is stretched tight between two clamps, and 100 wooden skewers are pressed across it, one every 2 cm. When the first skewer is twisted, the next skewer is pulled along a moment later, then the next, so a twisting wave travels down the line. Each skewer only swings up and down around the tape; what travels from one end to the other is the wave and its energy.

2A small motor with a crank arm twists the first skewer back and forth. A knob sets the frequency, the number of back-and-forth swings each second, in hertz (Hz). The length of the crank arm sets the amplitude, how far the tip of the first skewer swings from its resting position, in centimeters (cm). The team built two machines that are the same except for one thing: on machine B, a small ball of clay is pressed onto both ends of every skewer.

3To measure wavelength, Noemi filmed each machine in front of a wall marked in centimeters and measured the distance from one crest to the next. Anselm also timed single waves on machine A. A small swing of 2 cm and a large swing of 6 cm each took 1.25 s to travel the 2.0 m from the motor end to the far end.

4To measure energy, Mr. Lorne set up machine A so that its last skewer pushes a paddle on a toy motor that runs backward as a tiny generator. A meter adds up the energy that reaches the far end over 10 seconds, in millijoules (mJ). The team ran the motor at 2 Hz for every energy test and changed only the crank arm, and so the amplitude (bar graph).

5For the museum, the far end of machine A will tap a small bell. The bell rings clearly only when 30 mJ or more reaches the far end every 10 seconds.

Table 1: Wavelengths on the Two Machines
Frequency (Hz)	Machine A wavelength (m)	Machine B wavelength (m)
1	1.6	0.8
2	0.8	?
4	0.4	0.2

1.

Wave speed = frequency × wavelength. Use the 1 Hz row of Table 1. Do not round.

The waves on machine A travel at m/s.

2.

The waves on machine B travel at the same speed at every frequency. Use the other rows for machine B to find the missing value in Table 1.

At 2 Hz, the wavelength on machine B is m.

3.

Compare machine A with machine B at the same frequency. What did the clay balls change?

A. The waves on machine B moved faster, since the heavier skewers swung with more force.B. The wavelength on machine B stayed the same, but its frequency was twice as high.C. The waves on machine B moved at half the speed, so each wavelength was half as long.D. The motor swung more slowly on machine B, so its frequency dropped and its waves got shorter.

4.

Use your answer to question 2 or the other rows for machine B. A single crest leaves the motor end of machine B. Do not round.

It takes s to travel the 2.0 m to the far end.

5.

Use paragraphs 2 and 3 and Table 1. Match each change to the wave property it changes on the machine.

Part 2: Amplitude and energy

Use paragraphs 3 to 5 and the bar graph to answer the questions.

6.

Use the bar graph. The 6 cm amplitude is 3 times the 2 cm amplitude.

The energy that reached the far end with the 6 cm amplitude was times the energy with the 2 cm amplitude.

7.

Use the pattern in the bar graph. Suppose the team fits a crank arm that gives an amplitude of 8 cm, still at 2 Hz.

About mJ would reach the far end in 10 s.

8.

Noemi wants about 40 mJ to reach the far end in 10 s, twice the energy of the 4 cm amplitude, still at 2 Hz. Based on the bar graph, which amplitude is closest to what she needs?

A. About 5.7 cm, a little less than 6 cmB. About 16 cm, four times the 4 cm amplitudeC. About 4.5 cm, a little more than 4 cmD. About 8 cm, twice the 4 cm amplitude

9.

Anselm wants to test whether a bigger swing sends more energy. He suggests comparing a 4 cm amplitude at 1 Hz with a 2 cm amplitude at 2 Hz. What is the main problem with his plan?

A. He uses machine A, whose waves travel too slowly for the meter to measure their energy.B. He changes both the amplitude and the frequency, so he cannot tell which one caused a difference.C. He runs the motor at 1 Hz, which makes waves too long to fit on the 2.0 m machine.D. He keeps the amplitude the same in both of his runs, so the energy is going to come out the same.

10.

Use paragraph 5. Noemi wants to run the museum machine with the 4 cm amplitude, because "it is already twice the 2 cm swing, so it sends plenty of energy." Anselm wants the 6 cm amplitude. Which amplitude should the team choose for the bell? Write a claim, give evidence from the bar graph and paragraph 3, and explain your reasoning about amplitude and energy. Also say whether the bigger swing would make each wave reach the bell sooner.