# Engineering in Modern Medicine

## CONTENTS OF CURRICULUM UNIT 06.05.04

## Hold Off on the Headphones

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## Properties of Sound Waves

There are several characteristics that should be thoroughly understood to fully grasp the idea of longitudinal sound waves. These waves all have frequency, amplitude, wavelength and speed. At this point the teacher may want to introduce these concepts to the students. There are some wonderful websites that are available for educational use which provide video clips and interactive diagrams. See the website section at the end of the unit.

### Frequency

Frequency is the measure of "how often" a wave oscillates during a period of time. Frequency of a sound wave is measured in Hertz (Hz). One Hz is a measurement that describes a wave which makes a complete cycle in one second. Ten Hz is a wave that makes 10 cycles or vibrations in one second. We hear high valued frequencies as a higher pitch and lower frequency as a low pitch. Thus the rumble of thunder will have a lower frequency and a whistle will have a higher frequency. The normal range of frequency that a human can hear is between 20 Hz and 20000 Hz. In reference the range of the lowest not of a piano is 27.5 Hz and the highest note is 4186 Hz.

### Amplitude

Within a sound wave air molecules are compressed at each interval. The region of condensed air molecules creates an atmosphere of greater air density. In between these compressed regions are rarefied areas where there are fewer air molecules and a less dense atmosphere. The larger the difference in pressure between the compressed molecules and the rarefied molecules causes greater amplitude and a louder sound.

Amplitude measures how high and how low a wave moves in relation to the average of the wave. Amplitude of a sound wave is one half the difference of the highest pressure and the lowest pressure measured in the wave (1/2 (HP - LP)). Amplitude is therefore the measurement of pressure difference within a wave which results in the loudness of the sound.

Because the pressure difference is so small we measure the loudness of a sound wave with decibels (dB). Decibels measure the loudness of a sound just as amplitude does. The decibel scale is a logarithmic measure of sound pressure. Different than a linear measurement every increase of 20 dB means the pressure of the wave has increased 10 times greater in amplitude. At 20 dB the amplitude is 10, at 40 dB the amplitude is 10x10 =100, at 60 dB, the amplitude is 100x10=1000, etc. (Figure 1,2).

### Wavelength

Wavelength is the length of one complete cycle of a wave. In terms of amplitude it is the distance between two high pressure points.

### Speed of Sound

Speed of a sound wave measures how fast an oscillation travels from one place to the next. The speed of sound is about 660 miles per hour or 344 m/s at room temperature. In one complete cycle a wave moves forward one wavelength; therefore if we know the frequency of the sound wave and the wavelength then we can calculate speed of sound in air by using the formula:

(V = f/\) where V = speed, f = frequency and /\ = wavelength.

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Activity 3 Speed of Sound
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I will have students calculate the speed of sound in air. Students will be separated into groups of two. Each group will be given a cow bell, a pair of binoculars, a stopwatch and a measuring tape. I will have students stand 200m apart from each other. One student A will have the cow bell. Student B will be provided with the binoculars and the stopwatch. As the student A strikes the bell student B while looking through the binoculars will begin timing. Once student B hears the bell the timing will end. The speed of sound will be calculated by using the formula for velocity; velocity = distance / time.

Another activity that can be done with your students is to film or obtain video clips of lightening storms and have students measure the time they see the lightening and hear the sound of thunder. Have the student calculate the speed of sound by using the formula v = d / t. You can use a scale of 3 seconds per kilometer or 5 seconds per mile. This time interval corresponds to a speed of sound in air. For example if the time it takes between a flash of lightening and the sound of thunder on the video is 6 seconds then the speed of sound will be calculated by dividing 2 km / 6 s which would equal 1km/3s or 333.3 m/s (Hsu Tom, 2003).

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Activity 4 Properties of Sound Wave Calculations and Observations
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Students can now use the formula to calculate various problems for wavelength, frequency and speed. By knowing the speed of sound and the frequency, wavelength can be determined. Starting with the original given formula V = f/\ have student solve the equation for /\ (wavelength). This is a simple algebraic procedure which can be solved by isolating the variable by using the inverse operation. The students will have to divide both sides of the equation by "f" which will isolate /\ and give the new equation /\ = v/f (Hsu Tom, 2003).

Frequency can be described using a guitar and a tuner. Have the students use a guitar tuner to tune a guitar to standard tuning. Standard guitar tuning has the open notes tuned, from lowest pitch to highest pitch, to: E, A, D, G, B, E. Use a sound level meter to determine the frequency of each string. To tune the notes tighten or loosen the string according to the guitar tuner. This is a standard tuning sequence for many popular songs. Ask students to make observations about the pitch and frequency of each string after they have been plucked. Next have the students observe what happens to the frequency when you cause the string to become sharp and flat. Have students make observation on the how different frequencies of the same string cause a change in what they hear.

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A guitar is divided by frets. Holding down a finger on a string at different frets changes the wavelength of a plucked sting. This wavelength also changes the frequency of the sound. By using a guitar you can have students calculate wavelength by measuring the frequency of the plucked, fretted sting.

You could also go the music room and gather information of the various frequencies of each note on a piano and graph the information to provide a visual auditory representation of different frequencies. This can be done using a sound level meter. A sound level meter is an instrument that provides objective, reproducible measurements of sound pressure. It works very similar to the human ear. The meter will give you measurements in frequency and decibels. A bar graph can be draw with the keys on the x axis and the frequency on the y axis.

Students can then measure wavelengths, frequencies and amplitudes of musical instruments using sound. This will provide students with the ability to collect and analyze data. Students will use the sound and wave simulation software to examine the intensity and waveforms created from voice and musical instruments. Wave forms are then displayed on an oscillogram representing the wave of a physical sound. Students can print the graphs produced. Have student compare the wave patterns from different instruments tuned at the same frequency. Have students compare the wave patterns of the same instrument tuned at different frequencies.