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PURPOSE STATEMENT:

The purpose of the experiment was to calculate the speed of sound by measuring and using the

time it took for an echo to travel down and back a tube (of a certain length) that was closed on

one end, using a Vernier microphone and a computer. The distance that the echo traveled divided

by the time it took to get back to the source would be used as the speed of sound.

DATA:

Important Data (premeasured):

Length of Tube (m) 0.610

Total Length to be Traveled by the Sound (m) 1.22

Temperature of Room (degrees Celsius) 24.5

Echo Test Trials: Time Intervals From Initial Source of Sound to Reception of Echo

Trial Total Travel Time (s)

1 0.00346

2 0.00344

3 0.00344

4 0.00348

5 0.00340

Average 0.00344

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CALCULATIONS:

1. The following is a calculation of the average travel time of sound, or average time

interval between the creation of a sound and the reception of its echo, based on the data

collected in the Echo Test Trials.

Average Time Interval = Time1+Time2+Time3+Time4+Time5

Number of Trials

Average Time Interval =

(0.00346 s )+(0.00344 s )+ (0.00344 s )+(0.00348 s )+(0.00340 s)+(0.00344 s)5Trials

Average Time Interval = 0.00344 s

2. The following is a calculation of the speed of sound based on experimental/measured

values. The average time interval is used as the time value in the calculation.

Speed of Sound = DistanceTraveled ( twicethe lengthof the tube)

TimeTaken(average timeinterval)

Speed of Sound = 2(0.610m)(0.00344 s)

Measured Speed of Sound = 355 m/s

3. The following is a calculation of the theoretical value for speed of sound at a the

temperature at which the experiment was conducted.

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Theoretical Speed of Sound = 331.5 + 0.607(T)

Theoretical Speed of Sound = 331.5 + 0.607(24.5°C)

Theoretical Speed of Sound (at 24.5°C) = 347 m/s

4. The following is a calculation of the percent difference between the measured value for

speed of sound and the theoretical value for the speed of sound at 24.5°C.

Percent Difference = vs ( experimental )−v s( theoretical)

vs (theoretical) x 100%

Percent Difference = (355m /s )−(347m /s)

(347m /s) x 100%

Percent Difference = 2.31 %

CONCLUSION:

The experiment seemed to be pretty successful, as the measured value for the speed of sound at

24.5°C was very close to the theoretical value of sound. The measured value for the speed of

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sound was 355 m/s whereas the theoretical value for speed of sound was 347 m/s. The small

percent difference between the measured value and the theoretical value (2.31%) is further

indication that the measured value for sound is relatively close to the theoretical value of sound.

The results for the trials conducted to measure the time intervals between the production of a

sound and the reception of an echo are supporting evidence for the precision of the experiment.

As can be noted, the values measured for the total travel time (time interval) for each trial were

relatively close to each other. In Trial 1, the total travel time was recorded as 0.00346 s; in Trial

2, the total travel time was recorded as 0.00344 s; in Trial 3, the total travel time was recorded as

0.00344 s; in Trial 4, the total travel time was recorded as 0.00348 s, and in Trial 5, the total

travel time was recorded as 0.00340 s. The largest difference of total travel times was between

the value recorded in Trial 4 (0.00348 s) and the value recorded in Trial 5 (0.00340 s), and the

difference between the values is only 0.00008 s, a very small number in comparison to the values

for total travel time. This thus indicates that the conduction of the experiment was very precise.

Despite the fact that the experimental/calculated values were very close to the

theoretical/accepted values, there are various sources of error that could have made the

experimental values inaccurate. For example, the measurement for the temperature of the room

could have been inaccurate if the temperature probe was not calibrated or did not have enough

time to adjust to room temperature. Also, the measuring stick used to measure the length of the

tube may not have been precise enough for the experiment. Because the sides of the stick were

worn out, the measured length of the tube may have been longer than the actual length. Another

important factor to consider is that the aluminum foil used to cover one end of the tube was not

perfectly flat, leading to a concave or convex wall for the sound the bounce off of. If the

aluminum foil made a concave wall, the actual distance traveled by the sound would be less than

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the measured value, and if the aluminum foil made a convex wall, the actual distance traveled by

the sound would be greater than the measured value. Besides measurement error, there are other

sources for error in the conduction of the experiment. An example of this would be if the tube

was not placed on a flat surface when the experiment was conducted. The sound could rebound

off the sides of the tube, giving an inaccurate measurement for the travel time of sound. Along

Additionally, the person making the sound could have placed his or hand too far away from or

too far into the tube, causing the actual distance traveled by the sound to be greater or less than

the recorded/measured value. There are other sources for error in the experiment, but these are

some of the most significant to the accuracy of the experiment.

SUMMARY:

A wave is a vibration or disturbance in frequency. Periodic waves are waves that repeat, and a

pulse wave is a single wave. There are many types of waves in the world, including earthquakes,

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light, ocean waves, radio waves, and sound. Probably the most important classification for a

wave, however, is whether it is a transverse wave or a longitudinal wave. In a transverse wave,

the particles are disturbed in a direction perpendicular to wave motion, whereas in longitudinal

waves, the particles are disturbed in a direction parallel to wave motion. Sound is an example of

the latter, a longitudinal wave.

Sound is a form of travelling wave that is an oscillation of pressure through a certain medium:

solid, liquid, or gas. Sound is composed of frequencies that are within the range of hearing and in

the threshold of hearing. The speed of waves is dependent on the medium or material the wave is

travelling through as well as the wave type, and sound is not an exception. The accepted speed

for sound at 0 °C and through air is about 331.5 m/s. According to the following formula for

speed of sound in air, the speed of sound increases with temperature:

v = 331.5 + 0.607(T) m/s, where T = Temperature

In addition, sound travels fastest through solids, slower through liquids, and slowest through

gases. The speed of the wave can be determined by a generic formula:

v= λT

∨v=λ f

where λ = wavelength, T = period, and f = frequency

Period, frequency, wavelength, pitch, intensity, loudness, amplitude, and decibel level are

essential properties of sound. The period is the time it takes for an entire wave to pass a certain

point. Frequency is the reciprocal of period, and it is a measure of the number of waves that pass

a certain point in 1 second. Wavelength is the length of an entire wave, usually from the crest of

one wave to another or the trough of one wave to another. Pitch is directly related to frequency:

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the higher the frequency, the higher the pitch, and the lower the frequency, the lower the pitch.

Pitch is a representation of the perceived fundamental frequency of a sound. It is in a sense, a

way to compare waves of different frequencies. Intensity is the rate that energy flows through a

given area. Since power is the rate at which energy flows, intensity can be given by the formula

below:

I = PA

where I = intensity, P = power, and A = area

If the wave is spherical, the area through which the wave travels is the surface area of a sphere,

4πr2. The units for intensity are in W/m2 (Watts per meter-squared).

Intensity of a sound is related to loudness and amplitude. If amplitude is increased, then the

loudness of the sound is increased, and vice versa. Intensity is proportional to the square of

amplitude of a sound, and in sound waves, the amplitude of a sound wave is the change in

pressure as the wave passes by. Decibel level, or relative intensity, is a form of measurement

related to intensity. The Decibel level or scale is a logarithmic scale used to compare the

intensity of all sounds to the intensity of the softest sound that a human being can hear. The

softest sound that a human can hear (I0) has an intensity of 1 x 10-12 W/m2. An increase in 10 dB

(Decibels) is equal to increasing the intensity of sound by a factor of 10. The Decibel level of a

sound can be given by the following formula:

β=10 log ( II 0)

where β = Decibel level, I = Intensity, and I0 = Threshold of Hearing = 1 x 10-12 W/m2

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The formula could also be manipulated to solve for Intensity:

I = 10β

10 (I0)

Also important to the concept of sound is interference, or when more than one wave is in the

same place at the same time and they combine. The combined effect is the sum of the individual

waves, and this phenomenon is called superposition. There are two types of interference:

constructive interference and destructive interference. In constructive interference, waves come

together to form a larger wave. In destructive interference, the opposite happens—waves come

together to make a smaller wave. Beats are a special type of interference effect, where two waves

of slightly different frequencies interfere and there is an alternation between constructive and

destructive interference. This creates a variation in amplitude, or loudness. The beat frequency is

the difference between the two different frequencies:

fbeat = f1 – f2

Standing waves are examples of another type of interference effect. In standing waves, a fixed

pattern of vibration forms when two identical waves traveling in opposite directions interfere.

Harmonics are sets of half-wavelengths that will travel in a certain length of space. For

longitudinal waves, air particles are free to move and so the frequency of the wave can be found

by:

fn = nv

2L n = 1, 2, 3…

where n = harmonic number, v = speed of wave, and L = length wave is traveling across

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Music is different from noise in that music is more structurally organized, and there are much

fewer harmonics in the playing of a note than in a “noise.” Noise usually has many harmonics,

and the pure tone and pitch of musical notes is not present.

To talk about: Doppler Effect