Question

Like all our lab exercises, the waves and sound lab will use a PhET simulator. Some of these simulators require you to enable Java or Flash. You can download and use the simulator on your desktop, or for some labs you can run it in your browser. Preferred browser settings and system requirements can be found at the “Running Sims” FAQ:  https://phet.colorado.edu/en/help-center/running-sims (Links to an external site.)

For this lab, we’ll use the “Sound Waves” simulator:

https://phet.colorado.edu/en/simulation/legacy/sound (Links to an external site.)

This is a Java sim and will require a download of the software. Start the simulator, and spend some time learning the interface. We will be using the "Listen to a Single Source" and "Measure"tabs, so check out the interface in both. Understand the sliders, the pause function, and the measurement functions before you begin.

1. Use the Listen to a Single Source tab in Sound Waves to start your investigation of sound. Click Audio enabled so you can hear the sound.

• When you adjust the frequency on the slider, how does the sound change? How does the visual model of the wave change? Write your observations.
• When you adjust the amplitude on the slider, again observe how the sound changes and how the visual representation of the waveform changes, and record your observations.
• Do you think the frequency on the slider perfectly matches the visual waveform, or is some adjustment being made for the visualization? Describe what you think this adjustment might be, both qualitatively and in terms of the wave equation y ( x , t ) = y m sin ⁡ ( k x − ω t ).

2. Sound is produced when something vibrates; this movement causes disturbances in the surrounding air pressure. Investigate how the speaker cone moves to produce different sounds. Then, explain the relationships between the movement of the speaker cone and the sound that is made; include drawings to support your explanation. Record your observations and attach any necessary sketches as screenshots.

3. Use the tools on the Measure tab to find the speed of sound in air. Use the relevant equations to find which measurements you can make to discover the appropriate value.

Using a data table like the one below, record several measurements (at least 6-8 to minimize variance) of wavelength and frequency.

Trial	Wavelength (m)	Frequency (Hz)
1
2
3
4
5

4. Graph your data points in Excel or another graphing application, making sure to choose axes such that you get the speed of sound as the proportionality constant of the line. Refer to the wave speed equation to confirm this. Then, perform a fit to the line. Show the equation of the trendline on your graph and discuss whether you think the data you took accurately describes the relationship between wave speed, wavelength, and frequency.

Compare the value you found in your line fit to the actual, published value for the speed of sound in air, and include a percent error calculation. You can find the given value in several places, including your textbook and the internet - just make sure to cite your source properly. Use a temperature of 20 degrees C.

5. If you wanted to know the period of a wave, and did not have the frequency slider information available, could you find it with the tools in the simulator? Describe the method you would use to find the frequency (i.e. which measurements you would take, and which calculations you would perform).

6. Now, test the method you developed in part 5. Choose two frequencies and use your method to find the period. Record:

• the measurements you took, with appropriate units
• the calculations you did for each frequency.

Also, check to see how close you got - since period is the inverse of frequency (T = 1 f) then you can verify how well your method works. If it didn't work, describe any changes you would make to improve the results.

Lab Report:

Your lab report should be a typed document, with any necessary sketches or graphs attached as scans or picture files.

For the Sound Waves lab, hand in the following:

Part (a): Your preliminary observations and drawings from parts 1 and 2.

Part (b): Your data table and graph from part 3, and your calculated average speed, discussion of possible error, and citation for published speed of sound from part 4.

Part (c): A full description of the method you developed to find the period of a wave without knowing its frequency, including what measurements you would take and what calculations you would use. Also, your test of the method in full for two separate frequencies and your discussion of any errors and any changes you would make to the method.

Answer 1

When you adjust the frequency on the slider, how does the sound change? How does the visual model of the wave change? Write your observations.

When we increase the frequency, the sound gradually becomes sharp and and when we decrease the frequency, the sound gradually becomes flat.

When we increase the frequency, the sound waves appear to emitting quickly and when we decrease the the frequency, the sound waves appears to emitting slowly.

When you adjust the amplitude on the slider, again observe how the sound changes and how the visual representation of the waveform changes, and record your observations.

When we increase the amplitude, we start to hear high intensity sound and when we decrease the amplitude, we start to hear low intensity sound.

When we increase the amplitude, the the sound waves appears with high peaks and vallys and when we decrease the amplitude, the sound waces appears with low peaks and valleys.

Do you think the frequency on the slider perfectly matches the visual waveform, or is some adjustment being made for the visualization? Describe what you think this adjustment might be, both qualitatively and in terms of the wave equation .

When we adjust the frequency on the slider, the value of angular frequency is adjusted because in the wave equation, the is responsible for the frquency change.

Use the tools on the Measure tab to find the speed of sound in air. Use the relevant equations to find which measurements you can make to discover the appropriate value.
Using a data table like the one below, record several measurements (at least 6-8 to minimize variance) of wavelength and frequency.
Graph your data points in Excel or another graphing application, making sure to choose axes such that you get the speed of sound as the proportionality constant of the line. Refer to the wave speed equation to confirm this. Then, perform a fit to the line. Show the equation of the trendline on your graph and discuss whether you think the data you took accurately describes the relationship between wave speed, wavelength, and frequency.

The best-fit linear equation of the graph is given by:

Here,
value represents the value of wavelength
value represents the value of inverse frequency

The slope of the graph is:

The -intercept is :

We have relation between wavelength , frequency , and velocity of wave :

Therefore, the best-fit equation:

Therefore, the slope of the best-fit graph is equal to velocity of the wave:

Compare the value you found in your line fit to the actual, published value for the speed of sound in air, and include a percent error calculation. You can find the given value in several places, including your textbook and the internet - just make sure to cite your source properly. Use a temperature of 20 degrees C.

The speed of sound in air at , is

The percentage error speed of sound in air betwwen calculated and measured values is given by: