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Sound and Resonance Carolina Distance Learning

Investigation Manual

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Table of Contents

Overview……………………………………………………………………………………. 3

Objectives …………………………………………………………………………………………. 3

Time Requirements ……………………………………………………………………………. 3

Background ………………………………………………………………………………………. 4

Materials ……………………………………………………………………………………………. 9

Safety ………………………………………………………………………………………………. 10

Preparation ……………………………………………………………………………………… 10

Activity: Standing wave in a tube open at one end ………………………. 10

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Overview

In this activity, students will use a tuning fork to generate standing waves in a tube that

is open at one end and identify the length of tube necessary for the sound of the tuning

fork to be amplified through resonance, which is an increase in the amplitude of a

wave at a specific frequency. Through an understanding of the properties of waves

and the conditions necessary to establish standing waves in this scenario, students will

calculate the speed of sound in air at room temperature and the wavelength of sound

generated by the tuning fork.

Objectives

 Develop an understanding of the properties of waves

 Calculate the speed of sound in air at room temperature

 Generate a standing wave and demonstrate the property of resonance

Time Requirements

Preparation …………………………………………………………………………………..5 minutes

Activity 1 …………………………………………………………………………………….10 minutes

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Background

Waves can transmit energy over a great distance. Seismic waves generated by

earthquakes can cause extensive damage; scientists use their knowledge of seismic

waves to locate the epicenter of an earthquake. Sound and light are transmitted

through waves. Waves can also carry complex information over a long distance, for

example, radio waves. Some radios can send and receive complex signals and

broadcast over great distances. In this activity you will calculate the speed of sound in

air and apply some basic knowledge of waves to determine the wavelength of sound

generated by a tuning fork.

A wave is a propagation of energy due to a rhythmic disturbance in a medium or

through space. A medium is the material through which a wave travels. Mechanical

waves, such as waves in water, can only travel through a medium composed of some

form of matter. Sound waves are mechanical and can travel through a gas, such as

the air in earth’s atmosphere, liquid, and solid matter, but not through a vacuum.

Electromagnetic waves can travel through a medium, such as light waves through

glass, or through the vacuum of space, such as a radio signal.

A mechanical wave is transmitted when the molecules of a medium, such as air or

water, move or vibrate in a repeating or oscillating motion. The particles of the medium

generally remain in their original positions and vibrate back and forth, but the energy of

the wave travels outward from the wave source.

Mechanical waves can be classified as transverse or longitudinal. In a transverse wave

the particles of the medium move or vibrate in a direction that is perpendicular to the

direction of the wave. A group of people performing “the wave” in a stadium is a good

example of a transverse wave. People move their arms up and down (vertically), and

the wave travels horizontally around the stadium. When a string on a musical

instrument, such as a guitar or piano, is plucked or struck, the molecules in the strings

vibrate in one direction, whereas the energy in the wave travels along the length of the

string.

Sound travels in a longitudinal wave, also called a compression wave. When a sound

wave is generated, the molecules of the medium vibrate in a direction parallel to the

direction of the wave, but do not travel with the wave, remaining in the same location.

When a sound is generated, e.g., by the tuning fork in this activity, the air near the

source vibrates, causing a disturbance in the surrounding air molecules that travels

outward in all directions, but the air molecules near the source and along the wave

generally remain in their original locations.

Longitudinal mechanical waves travel through solids, liquids, and gases; however

transverse waves only travel through solid or liquid matter.

The intensity and frequency of a wave are functions of the wave source, whereas the

speed of the wave is determined by the medium through which the wave travels. To

better understand waves, consider the diagram in Figure F1.

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Figure F1.

The horizontal line is called the rest position. This is where the particles in the medium

rest until disturbed by the energy from the wave. The distance labeled A is the

amplitude of the wave. The amplitude of the wave is directly related to the intensity, or

acoustic energy, of the sound. For a sound wave, greater amplitude means louder

sound. The amplitude is the distance from the rest position to the position of greatest

displacement. The position of greatest displacement above the rest position, the

highest point on the wave, is the crest. The position of greatest displacement below the

rest position is the trough. The wave height (WH) is twice the amplitude. The distance

between any two identical points (i.e., two crests or two troughs) on a waveform is the wavelength and is represented by the Greek letter lambda (λ). In depictions of

waveforms the wavelength is usually depicted between two crests, as in Figure F1.

The waveform in Figure F1 can represent any kind of wave. The amplitude and

wavelength provide enough information to analyze the wave. You may have seen

sound waves represented by this type of waveform on an oscilloscope or computer

screen.

In a sound wave, which is a compression wave, the air molecules move together in

regions called compressions, and spread apart in regions called rarefactions (Figure F2).

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Figure F2.

Another important property of waves is frequency. The frequency is the rate at which

the particles in the medium vibrate. Frequency is measured in Hertz (Hz; cycles per

second, cycles/s, cycles × s-1). Try tapping an object, such as a pencil, on a surface, such

as a table, at a rate of one tap per second. That is a frequency of 1 Hz. The inverse of

wave frequency is the period of the wave. If you tap the pencil at a frequency of 2 Hz

or two taps per second, the period, or time between taps is 0.5 s. What is the highest

frequency at which you can tap the pencil? The tuning fork in this kit has a frequency of

2048 Hz. Humans can hear sounds in a frequency range of 20–20,000 Hz. Anything above

the range of human hearing is called ultrasound, and anything below is called

infrasound. A dog whistle makes an ultrasonic sound that is too high for humans to hear,

but within the audible range for dogs. As people age, the ability to hear the higher

frequencies diminishes.

The velocity, or speed, of a wave is related to the wavelength and frequency as

described in the equation:

v = fλ

where v is velocity in meters/s; f is frequency in Hz, and λ is wavelength measured in

meters.

For example, consider a wave with a wavelength of 0.5 m and a frequency of 27 Hz.

𝒗 = (0.5𝑚)(27 𝐻𝑧)

𝒗 = 13.5 𝑚/𝑠

Waves exhibit many phenomena:

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 Echo Waves reflect off solid objects.

 Diffraction Waves diffract, or bend, around solid objects. An example of this is

waves bending when passing through a gap, such as ocean waves passing

between barrier islands.

 Interference Waves interact with other waves. Imagine two instruments, such as

trumpets, that are slightly out of tune, or have a slightly different pitch. Both

trumpets play the same note, but the wave forms leaving each instrument are

out of sync. The result is an oscillation in the intensity or loudness of the sound.

Two sound waves result in a tone that has “beats” of higher and lower volume.

 Standing waves: At certain frequencies, a wave source may create waves that

reflect back from one end of a medium and interfere with waves emanating

from the source. A wave pattern is established where every point on the wave

has a constant amplitude. A simple demonstration of a standing wave can be

created with a rope or string. Tie a rope to a post or other immovable object.

Pull the rope tight and then move it rhythmically up and down. Vary the speed

of movement until the rope generates a constant wave form similar to that

shown in Figure 4. The wave pulses travel from the wave source, your hand, to

the post and reflect back. At a particular frequency, the wave appears to stand

still. In this example, the frequency depends on the linear density of the rope

(mass per unit length; g/cm) and the tension. If you are having trouble setting up

a standing wave with a rope, try adjusting the tension.

Where the wave forms cross, there is no displacement of the rope. These points

are called nodes. The rope is maximally displaced halfway between two nodes.

These points are called antinodes. Because you are moving the rope at one

end, that end is an antinode. The end at which the rope is anchored is a node.

Try changing the frequency of the wave. Each new frequency will be

associated with a different standing wave pattern, with different numbers of

nodes and antinodes. These frequencies and the associated wave patterns are

called harmonics.

Figure F3 shows how standing waves are established in an air column in a tube

that is open at both ends. Each harmonic is an integral multiple of the first

harmonic, or fundamental frequency. If the velocity of air is known and the

length of the column can be measured, the frequency of each harmonic can

be calculated.

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Figure F3.

Figure F4 shows how standing waves are established in a tube that is closed at

one end. There will be a node at the closed end of the tube and an antinode at

the open end. Whenever the frequency of the wave is an odd-numbered

integral of the fundamental frequency, a standing wave will be established in

the tube.

Figure F4.

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Materials

Included in the Sound and Resonance kit:

Tuning fork, 2048 Hz

Plastic tube, open at both ends

Needed from the Central Materials set:

Graduated cylinder, 2 parts, unassembled

Ruler, metric

Needed, but not supplied:

Calculator

Permanent marker

Reorder Information: Replacement supplies for the Sound and Resonance investigation

can be ordered from Carolina Biological Supply Company, kit 580406.

Call 1-800-334-5551 to order.

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Safety

Read all instructions for this laboratory activity before beginning. Follow the

instructions closely and observe established laboratory safety practices, including

the use of appropriate personal protective equipment (PPE) described in the Safety

and Procedure sections.

Do not eat, drink, or chew gum while performing this activity. Wash your hands with

soap and water before and after performing the activity. Clean up the work area

with soap and water after completing the investigation. Keep pets and children

away from lab materials and equipment.

Preparation

1. Go to a quiet location with enough workspace to place the graduated cylinder on

a flat surface. Strike the tuning fork against your hand and hold it at arm’s length. If

you cannot hear the tuning fork, move to a quieter location.

2. Use your ruler and permanent marker to mark the entire length of the clear plastic

tube at 1-cm intervals. Allow time to dry.

In the following activity you will measure the speed of sound in air. Using the tuning fork

as a sound source and a tube, one end of which is submerged in water in a graduate

cylinder, you will adjust the length of the air column in the tube until a standing wave is

established. When the standing wave is set up, the tube will resonate, which amplifies

the sound slightly. You will then be able to calculate the wavelength of the standing

wave.

Activity: Standing wave in a tube open at one end

1. Calculate the speed of sound in the surrounding atmosphere. Measure the

temperature of the room using the thermometer, and use the following equation.

𝑣𝑠 = 331.4 + 0.6𝑇𝐶

where vs = the speed of sound in meters per second (m/s), 331.4 m/s is the speed of

sound in air at freezing temperatures, and Tc = the temperature of the room in

degrees Celsius. 0.6 is a constant with dimensions of, m/s/°C.

Record TC and vs values in the Data Table.

2. Assemble the graduated cylinder by placing the cylinder in the base.

3. Fill the graduated cylinder to the top with water.

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4. Place the plastic tube in the cylinder. The submerged end is the closed end of the

resonance tube, and the end above the surface of the water is the open end.

5. Strike the tuning fork on the palm of your hand or a book and hold the vibrating

tuning fork about 2 cm (~¾ in) above the mouth of the plastic tube.

6. Raise the plastic tube, increasing the length of the air column in the tube, while

keeping the tuning fork about 2 cm above the mouth of the tube.

7. Listen for the point at which the plastic tube amplifies the sound from the tuning fork.

It may be necessary to strike the tuning fork again during the experiment if the

sound becomes too faint, and it may be necessary to move the tube up and down

to reach to find the exact point where the sound from the tuning fork is amplified.

8. Measure the distance from the open end of the tube to the water. This is the length

of ¼ of one wavelength. Record this value (L1) in Data Table.

9. Continue moving the tube upward, further extending the length of the air column,

until you reach the next point where the sound from the tuning fork is amplified. This

is the length of ¾ of one wavelength. (See Figure 6) Record this value (L2) in Data

Table.

10. Move the tube upward again until you reach the next point where the sound from

the tuning fork is amplified. This is the length of 5/4 of one wavelength. Record this

value (L3) in Data Table.

11. Complete Data Table, using the speed of sound in the air (vs) to calculate the

length of the wavelength, λ.

12. Calculate the percent difference between the values you calculated for the

speed of sound using the closed tube and the equation from step 1 using the

equation:

𝑣𝑠 = 331.4 + 0.6𝑇𝐶 v = fλ

% 𝑑𝑖𝑓𝑓𝑒𝑟𝑒𝑛𝑐𝑒 = | 𝑓𝑖𝑟𝑠𝑡 𝑣𝑎𝑙𝑢𝑒 − 𝑠𝑒𝑐𝑜𝑛𝑑 𝑣𝑎𝑙𝑢𝑒

( 𝑓𝑖𝑟𝑠𝑡 𝑣𝑎𝑙𝑢𝑒 + 𝑠𝑒𝑐𝑜𝑛𝑑 𝑣𝑎𝑙𝑢𝑒

2 )

| 𝑥 100%

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Figure 6

Data Table

Temperature

(°C)

vs*

(m/s)

f

(Hz)

Length (L)

(m)¶

Calculate

λ§

(m)

Vs**

(m/s)

2048

L1

(L1=λ/4 and λ=4L1)

L2

(L2=3λ/4 and λ=4L2/3)

L3

(L3=5λ/4 and λ=4L3/5)

*Speed of sound in air (vs) = 331.4 + 0.6TC.

**Speed of Sound in air (vs) = fλ ¶Convert cm measurements to m. §Using equation vs = fλ and/or λ = vs/f.

NAME:_________________

Lab # 6 : Colour – Magnitude Diagram for M 45 (Pleiades)

Introduction: The Pleiades is a relatively close open cluster. The six or seven stars visible to the naked eye form a tight grouping of stars (an asterism) near the even closer Hyades cluster. They are easily visible in the summer months from the southern hemisphere. In this exercise, you will determine the colour of many cluster members and plot them on a Colour-Magnitude diagram. This is just a type of Hertzsprung-Russell (HR) diagram in which we plot Colour Index rather than Spectral Class on the horizontal axis; and use the apparent visual magnitude, V, for the vertical axis.

Procedure: Photometric measurements of the Pleiades cluster can be used to determine the age of the cluster and its distance. By taking images of the stars through separate blue (B) and visual (V) filters we can measure the apparent magnitude of each star in each waveband colour. In this exercise this stage has already been done, presenting you with a table with two magnitude values for each star. You may recall that a visual or V filter approximates the spectral response of the human eye and is most sensitive in the yellow part of the spectrum. A blue filter, B, which corresponds to the sensitivity of photographic film (hence photographic magnitude).

The data reductions and plotting below can be done either manually or using a spreadsheet.

1. Calculate and record the Colour Index for each star in table below, the other two columns will be done later. The colour index or CI is found by the following equation:

CI = B – V

Photometric Data for Pleiades (M45):

Star no. V mag

(mV) B Mag CI = B – V

Abs V

(MV)

1 10.44 11.06 2 7.52 7.62 3 6.60 6.57 4 7.97 8.15 5 5.09 5.01 6 3.64 3.56

7 8.12 8.34 8 11.35 12.13 9 6.95 7.07 10 10.91 11.77 11 9.05 9.54 12 10.02 10.58 13 8.27 8.63 14 9.25 9.80 15 9.88 10.42 16 7.66 7.87 17 10.48 11.12 18 6.81 6.87 19 2.87 2.78 20 6.29 6.31 21 8.25 8.51 22 8.69 9.15 23 7.26 7.31 24 6.99 7.02 25 6.82 6.84 26 12.61 13.79 27 9.46 9.93 28 8.37 8.67 29 9.29 9.75 30 12.12 13.14 31 11.71 12.58 32 10.42 11.06 33 11.34 12.20 34 12.89 13.68 35 7.35 7.45 36 7.96 8.28 37 4.18 4.12 38 9.70 10.25 39 5.76 5.72 40 6.43 6.41 41 8.60 8.95 42 11.27 12.19 43 3.88 3.81 44 7.18 7.34

45 9.45 9.97 46 10.55 11.22 47 10.13 10.75 48 8.04 8.25 49 7.85 8.05 50 4.31 4.20 51 10.39 11.02 52 5.46 5.42 53 8.58 8.92 54 11.40 12.25 55 3.71 3.60 56 10.81 11.61 57 11.93 12.87

2. Plot your results as an “X – Y” scatter plot, using “V mag” for the vertical axis and “B – V” for the horizontal axis. Remember to draw your vertical scale so that the lower the value of “V mag”, the higher up the axis it is (in spreadsheet reverse order of values). Ensure that you have clearly marked the scales. Give yourself enough room above and below your vertical scale values to add additional data later.

Questions after done the plot:

1. What is the trend of the majority of stars in the Pleiades cluster?

2. In blue, circle the most massive star/s on your Colour-Magnitude plot, these are to the left.

3. In red, circle the least massive group of stars on the diagram, these are to the right.

4. Draw a curve to the trend of these stars, name this trend “Main Sequence” (it should look like an “S” shape)

5. Look on the Internet for a color image of the Pleiades Cluster (M45). Comment on the neatness of the image. Are they young or old? How can you tell? Explain: (hint: see the presence of molecular dust/gas around them)

6. Look at the photo of the Pleiades below.

The Pleiades Open Cluster, M45.

Is there any visible evidence to support your answer to questions 5? What does

this evidence suggest about the origin of stars? (think on molecular clouds)

7. In this exercise, you have plotted apparent magnitude V-mag (or mv), rather than absolute magnitude, Mv, or Luminosity on the vertical axis. Let’s make a strong assumption about the stars in the Pleiades cluster that it is about 126 parsecs away from us (observers). Results from the European astrometry satellite, HIPPARCOS, gave a distance of 116 parsecs to the Pleiades. So, using the distance modulus equation:

𝑀 = 𝑚 − 5   ∙   log ( ! !” )

Calculate the Absolute (visual) Magnitude, M of each of the Pleiades stars, in table above (5th column)

8. Make a new plot with the vertical axis (the scale) using the Absolute Magnitude (5th column entries). Again, lower number up and higher numbers down (reverse axis values – flip).

9. The value ”m – M” is called the distance modulus. What is the value for all the Pleiades stars? (calculate the distance modulus for five rows in table above)

10. Would the value of the distance modulus for a more distant cluster be higher or lower? (Example: use distance 200 pc equation above). Explain:

11. The relationship between Colour Index (CI) and Spectral Class for Main Sequence stars (ie those of Luminosity Class V) is shown in the table below. Use it to mark in the values for spectral class beneath those of colour index values on your plots (x-axis) from steps 2 and 8.

Spectral Class B – V

B0 -0.31

B5 -0.16

A0 0.00

A5 +0.13

F0 +0.27

F5 +0.42

G0 +0.58

G5 +0.70

K0 +0.89

K5 +1.18

M0 +1.45

12. On your plot, write in the colour (eg, red) beneath the corresponding spectral class (see charts in textbook chapter 13)

13. Using the capital letter SUN, mark in where the Sun would be on your plot (use plot in step 8).

14. Draw and label three regions on your plot to show where red giants, red supergiants and white dwarfs would be found in both plots

15. Below is a colour-magnitude diagram for the globular cluster, M5.

Credit: SEDS (C-M diagram) and AAO (image)

Is the globular cluster older or younger than the open clusters? Justify your answer: