General Physics Lab Department of PHYSICS YONSEI University

Lab Manual (Lite)

Mechanical Waves Ver.20180424

Mechanical Waves

Experiment 1. Standing Waves on a String, Part 1

In this experiment, the length 𝐿𝐿 of the string and the tension 𝐹𝐹 on the string are held constant as the frequency 𝑓𝑓 is var-ied. (1) Set up the equipment. Set up the equipment as below, and place the black screen behind the string for easy observation of the wave pattern. Insert the string in the slot on the top of the string holder of the wave driver so the wave driver can cause the string to vibrate up and down. Gently press or hold the string of the left-side of the wave driver so this part of the string does not vibrate. If the string has knots on it, unravel the knots.

(2) Run Capstone software. ① Click [Signal Generator] in the [Tools] palette. ② Select [850 Output 1]. ③ Select [Sine] for [Waveform]. ④ Set [Frequency] and [Amplitude].

- [Frequency]: 20Hz - [Amplitude]: 5V or less (Do not exceed 5V.) ⑤ Use [On] or [Off] buttons to operate the wave driver.

NOTICE This LITE version of manual includes only experimental procedures for easier reading on your smartphone. For more information and full instructions of the experiment, see the FULL version of manual.

Procedure

Caution 1. Be careful not to make knots on the string. If the string has knots on it, please unravel the knots. (Do not unrav-el the loop knots at the ends.) 2. DO NOT cut the string. 3. Keep the string in the plastic bag.

(3) Exert a tension on the string. Hang about 1.0 kg mass to the end of the string (use an

electronic balance to measure mass with accuracy). Calcu-late this tension 𝐹𝐹 = 𝑚𝑚𝘨𝘨. (4) Measure the length of the string. Use the ruler to measure the length 𝐿𝐿 between the string holder of the wave driver and the top of the pulley. (5) Turn on the wave driver. Click [On] in the [Signal Generator] panel.

(6) Find the fundamental frequency (𝑛𝑛 = 1). Vary the output frequency of the signal generator until the string vibrates in one segment (the fundamental frequency).

(7) Find the frequencies required for the higher harmonics. In the same way, vary the output frequency of the signal

generator until the string vibrates in each of the higher har-monics (𝑛𝑛 = 2, 3, 4, … ) and record these frequencies.

𝑛𝑛 1 2 3 4 ⋯

𝑓𝑓𝑛𝑛

(8) Find 𝜇𝜇 of the string. Plot a 𝑓𝑓 - 𝑛𝑛 graph and find the slope of the graph using the

method of least square. Finally use Eq. (5) to calculate the linear mass density 𝜇𝜇 of the string.

𝑓𝑓𝑛𝑛 =𝑛𝑛

2𝐿𝐿�𝐹𝐹𝜇𝜇 = �

12𝐿𝐿

�𝐹𝐹𝜇𝜇� 𝑛𝑛 (𝑛𝑛 = 1, 2, 3, … ) (5)

(9) Analyze your result. The direct calculation of 𝜇𝜇 is 𝜇𝜇ref = 3.34 × 10−4 (kg/m) , which is calculated by dividing the real mass (1.67 × 10−2 kg) by the length (50 m) of the string. (10) Repeat the experiment. Change mass to 0.5 kg and repeat steps (3) to (9).

Experiment 2. Standing Waves on a String, Part 2 In this experiment, the frequency 𝑓𝑓 and the tension 𝐹𝐹 on

the string are held constant as the length 𝐿𝐿 of the string is varied. (1) Set up the equipment. Use the setup detailed in expt. 1. Place the wave driver near the pulley. Hang about 0.5 kg mass to the end of the string.

(2) Set up Capstone software. Use the setup detailed in expt. 1. Set [Frequency] of [Signal Generator] at 𝑓𝑓 = 150 Hz and do not change it. (3) Turn on the wave driver.

(4) Vary the length 𝐿𝐿 of the string. Move the wave generator away from the pulley until the string vibrates in one segment (the fundamental frequency). Keep holding the string of the left-side of the wave driver so this part of the string does not vibrate. (5) Find the length 𝐿𝐿 required for the higher harmonics. In the same way, vary the length of the string until the string

vibrates in each of the higher harmonics (𝑛𝑛 = 2, 3, 4, … ) and record these lengths.

𝑛𝑛 1 2 3 4 ⋯

𝐿𝐿

(6) Find 𝜇𝜇 of the string. Plot a 𝐿𝐿 - 𝑛𝑛 graph and find the slope of the graph using the

method of least square. Finally use Eq. (5) to calculate the linear mass density 𝜇𝜇 of the string.

𝑓𝑓𝑛𝑛 =𝑛𝑛

2𝐿𝐿�𝐹𝐹𝜇𝜇 𝑜𝑜𝑜𝑜 𝐿𝐿 = �

12𝑓𝑓

�𝐹𝐹𝜇𝜇� 𝑛𝑛 (𝑛𝑛 = 1, 2, 3, … ) (5)

(7) Analyze your result.

Experiment 3. Standing Sound Waves, Part 1 (1) Set up the equipment.

Caution 1. Be careful not to make knots on the string. If the string has knots on it, please unravel the knots. (Do not unrav-el the loop knots at the ends.) 2. DO NOT cut the string. 3. Keep the string in the plastic bag.

(2) Set up Capstone software. (2-1) Add a [Voltage Sensor].

(2-2) Add an [Output Voltage Current Sensor].

(2-3) Configure the signal generator. Set the parameters of [850 Output1] as below. [Waveform]: Sine [Frequency]: 800 Hz

[Amplitude]: 0.5~1.0 V Do not exceed 1.0V. You can damage the speaker.

[Auto] (automatically starts or stops the generator.)

(2-4) Select [Fast Monitor Mode] in the controls palette. [Fast Monitor Mode] displays data without recording. Check

that [Recode] button is changed to [Monitor] button. Do not use [Continuous Mode]. It collects lots of data and causes a hang or freeze of the software.

(2-5) Create a scope display. Click and drag the [Scope] icon from the [Displays] palette into the workbook page.

(2-6) Add an independent 𝑦𝑦-axis to the scope display. Click [Add new y-axis … ] to make a two-channel scope.

(2-7) Define the axes. 𝑥𝑥-axis: Time(s) 𝑦𝑦-axis(left): Output Voltage, Ch01 (V)

(Signal Generator Output, or Speaker Input) 𝑦𝑦-axis(right): Voltage, Ch A (V)

(Voltage Sensor Reading, or Microphone Output)

(3) Demonstrate monitoring data. (3-1) Click [Monitor] in the controls palette.

(3-2) Turn on trigger. Click [Activate … trigger] in the toolbar to horizontally align

repetitions of the signal.

(3-3) Scale the display

① Speaker Input (Signal Generator Output): Drag the scaling pointer on the left 𝑦𝑦-axis. ② Microphone Output (Voltage Sensor Reading): Drag the scaling pointer on the right 𝑦𝑦-axis. ③ Time (Period): Drag the scaling pointer on the 𝑥𝑥-axis. (3-4) Find the axis of each trace. When the scale fits data, you can see two traces as below. Each trace has a random color. Color in legend matches plot color. For example, in the figure below,

Color Symbol Measurement Axis

Blue Vo Output Voltage, Ch 01 (V)

(Speaker Input) Left 𝑦𝑦-axis

Orange V Voltage, Ch A (V)

(Microphone Output) Right 𝑦𝑦-axis

(4) Make a stopped pipe. Generally, a stopped pipe is considered to be a pipe that is closed at one end and open at the other. In keeping with this convention, the speaker should be positioned several centi-meters back from the end of the tube, so the speaker end of the tube is open.

(5) Turn on the microphone.

(6) Begin your experiment. Click [Monitor].

Move the piston to a position near the speaker end of the tube, and then slowly pull the piston plunger, until you hear the sound from the speaker being amplified by the tube, indi-cating that you have produced a standing wave in the tube. Adjust the piston position carefully until you find the first point (𝑛𝑛 = 1) which produces the loudest sound. (You can also find the relative maximum by watching the trace on the scope display.) Record this position. Now continue moving the piston until you have found all of the piston positions (𝑛𝑛 = 3, 5, 7, 9, … ) along the tube which produce standing waves. (7) Find the speed of sound.

The open end of the tube is always a displacement antinode, so theoretically 𝐿𝐿𝑛𝑛=1 = 𝜆𝜆 4⁄ as above. However, the dis-placement antinode actually occurs somewhat beyond an open end of the tube. Thus, we cannot find 𝜆𝜆 by using Eq. (6). Other equations such as 𝐿𝐿𝑛𝑛=3 − 𝐿𝐿𝑛𝑛=1 = 𝜆𝜆 2⁄ , give a more accurate calculation for 𝜆𝜆 of the standing wave in the tube.

𝐿𝐿𝑛𝑛=1 𝐿𝐿𝑛𝑛=3 𝐿𝐿𝑛𝑛=5 𝐿𝐿𝑛𝑛=7 ⋯

1st

2nd

3rd

𝐿𝐿𝑛𝑛=3− 𝐿𝐿𝑛𝑛=1

𝐿𝐿𝑛𝑛=5− 𝐿𝐿𝑛𝑛=3

𝐿𝐿𝑛𝑛=7− 𝐿𝐿𝑛𝑛=5

⋯ AVG

(= 𝜆𝜆 2⁄ )

1st

2nd

3rd

𝜆𝜆 _______ (m)

𝑓𝑓 _______ (Hz = s−1)

𝑣𝑣result 𝑣𝑣 = 𝜆𝜆𝑓𝑓 (m/s)

𝑣𝑣ref. 𝑣𝑣air = 331.3 + 0.606𝑇𝑇 (m/s)

(8) Repeat the procedures above for = 1000 Hz .

𝑣𝑣air = 331.3 + 0.606𝑇𝑇 (m/s)

Note The accepted value of the speed of sound in air is ( 𝑇𝑇 : temperature in Celsius degrees)

Experiment 4. Standing Sound Waves, Part 2

Set the output frequency at 𝑓𝑓 = 800 Hz. Adjust the position of the piston so a 𝑛𝑛 = 5 standing wave is produced. Use a twist tie to mount the microphone on the end of the

probe rod, and insert it into the tube through the hole in the speaker stand. As you move the microphone down the length of the tube, note the positions where the scope signal is a maximum and where it is a minimum. Use the data to sketch the wave activity along the length of the tube and to find the speed of sound. Pay particular attention to the wave characteristics near the open end of the tube and describe it.

Please put your equipment in order as shown below. □ Delete your data files from the lab computer. □ Turn off the Computer and the Interface. □ Turn off the Microphone. Conjoin the microphone, the audio connector, and the converter. □ Keep the Sting in the plastic bag. Be careful not to make knots on the string. □ Plug the slotted String holder to the arm of Wave Driver.

End of LAB Checklist

Caution Please turn off the microphone.