## Sound

Sound is a longitudinal wave produced by vibration. Sound waves require a medium hence, they cannot be transmitted in a vacuum as can electromagnetic waves. The particles in the medium collide transmitting pressure waves away from the source of the vibration.

The areas in the medium that become packed closely together are called compressions. The areas where the medium particles are spread out are called rarefactions.

The velocity of sound waves depends on the temperature of the medium. On the average, sound waves in air travel about 343 m/s. Sound can travel through liquids and solids and can be diffracted, spreading outward after passing through narrow openings. Interference can occur between sound waves producing louder (increased amplitude) sound or cancel each other out, creating "dead spots", where no sound is heard (zero amplitude).

The change in the wavelength of sound emitted by a moving source is called the Doppler Effect. When the source is moving toward the detector (e.g., your ears), the wavelength shortens thereby increasing the frequency and the sound. When the source moves away from the detector, the wavelength gets longer resulting in a decrease in sound and frequency. The equation for the Doppler effect is:

### fd = fs (v + vd/v - vs)

where vd is the speed of the detector, vs is the speed of the source, fs is the frequency of the source, and fd is the frequency of the detector.

Pitch is a quality of frequency. Loudness is a function of amplitude. Musical notes are associated with specific frequencies. The higher the note, the higher the frequency. The louder the sound, the higher the amplitude. When two notes are separated by a frequency ratio of 2:1 the difference is called an octave. Sound level is measured in decibels (dB). It is the ratio of the intensity of a sound the faintest sound audible (0 dB). A sound that is 10 times louder than the faintest sound is 10 dB and one that is 100 times louder than the faintest sound is 20 dB. Twenty dB's is 10 times louder than 10 dB.

Musical instruments rely on resonance to produce certain pitches. Resonance is increasing the amplitude of a vibration by repeatedly applying a small external force at the same frequency. A closed pipe resonates when its length is 18/4, 38/4, 58/4, etc.. An open pipe resonates if its length is 18/2, 28/2, 38/2, etc.. Standing waves are produced in closed pipes. The separation in standing waves between two nodes, or two antinodes, is 1/2 wavelength. If open and closed pipes of the same length are used, the wavelength of the resonant sound for the open pipe will be half that of the closed pipe. Therefore the frequency for the open pipe will be twice as high as that for the closed pipe.

### Diagram: Closed ended pipe.

Most sound is made up of multiple frequencies. The relative intensities of these frequencies is the sound quality or timbre. A pulsing variation in loudness caused by two slightly different frequencies is called a beat. The human ear can detect beat frequency up to 7 Hz. If two waves differ by more than 7 Hz, a complex wave is heard which may be unpleasant (dissonant) or pleasant (consonant). Consonance is called a chord.

The lowest frequency making up a sound is called the fundamental. Higher frequency waves are called overtones. The intensity of the overtones is usually less than that of the fundamental. An open pipe resonates when the length is an integral number of half wavelengths (8/2, 28/2, 38/2, ...). The frequencies produced by an open pipe system with fundamental frequency f are f, 2f, 3f, etc..

### Review Questions:

1. While listening intensely to a physics lecture, a piece of ceiling falls on Cleather's head. What is the frequency of the sound produced if the wavelength is 0.667m?

514 Hz

2. Celita can detect sounds between 20 Hz and 16 kHz. What is the largest and smallest wavelengths she can detect at room temperature?

Largest wavelength = 17 m. Smallest is 0.021 m.

3. Donathon shouts outside on the field and hears an echo 0.20 s later. How far away is the wall the sound bounces back from?

34 m

4. Josh is looking for a speaker that will produce a frequency around 1 kHz. He tests out a woofer that is 38 cm in diameter and a tweeter that is 7.6 cm. The sound has a wavelength equal to the diameter of the speakers at room temperature. Which one will produce the frequency he is looking for?

Woofer is 0.90 kHz. Tweeter is 4.5 kHz.

5. Gladis sings through an open pipe filled with Helium and finds resonances spaced by 20.2 cm. What is the frequency of her voice? The speed of sound through Helium is 347 m/s.

859 Hz

6. Amanda shouts in a canyon valley. Assuming parallel vertical walls, she hears the echo from one wall 2.0 s later. The echo from the other wall is heard 2.0 s after the first echo. How wide is the valley?

1.0 km

7. Scott is driving his car at 31 m/s down the street when Aaron steps out in front of him. He blows the horn which has a frequency of 305 Hz. What is the frequency that Aaron hears?

335 Hz

8. Trevor is playing chicken with Derek in his car. Trevor is driving at 31 m/s and Derek is heading straight for him at 21 m/s. If Trevor blows his 305 Hz horn, what frequency horn does Derek hear?

356 Hz

9. Suppose Eugene, going 31 m/s, decides to run into the back of Ellen, who is driving away from him at 21 m/s. If he blows his 305 Hz horn at her, what frequency horn does she hear?

315 Hz

10. Lynn goes to a Korn concert and the band plays at 80 dB. How many times greater is the sound pressure from Rob Zombie which plays at 120 dB?

100x

### Honors

11. If you went hiking and found an abandoned mine and dropped a stone into a mine shaft 122.5 m deep, how soon after you drop the stone do you hear it hit the bottom of the shaft?

5.36 s

12. You are at homecoming and, while playing trumpet on a moving float hit an A note (440 Hz) while at the same time a guy sitting in the bleachers with the band hits the same note. You hear 3 beats per second. How fast are you moving toward the trumpet player in the bleachers?

2.3 m/s

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