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# Sound

## Longitudinal vibrations through the air are perceived by us as sounds.

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Sound

Sound waves are longitudinal waves. Thus, the molecules of the medium vibrate back and forth in the same direction as the wave is traveling through. The medium for sound is normally air for humans, but sound waves can travel in water, metal, etc. as well. An object oscillating with frequency f\begin{align*}f\end{align*} will create waves which oscillate with the same frequency f\begin{align*}f\end{align*}. The speed of a sound wave in air depends subtly on pressure, density, and temperature, but is about 343 m/s at room temperature.

Key Equations

T=1f\begin{align*}T = \frac{1}{f}\end{align*} ; period and frequency are inversely related

v331.4 m/s+0.6 T\begin{align*}v \approx 331.4 \ m/s + 0.6 \ T\end{align*} ; The speed of sound in air, where T\begin{align*}T\end{align*} is the temperature of the air in Celsius

#### Example

Describe the pressure changes in the air as a sound wave passes a given point, then explain why a very loud sound can damage your tympanic membrane (ear drum).

As a sound wave passes a certain point, the air pressure at that point alternates between high and low pressure. When sound waves pass into the ear, the alternating pressures cause a pressure difference on either side of the tympanic membrane. The pressure differences between the inside and outside of the membrane cause the membrane to move back and forth with the same frequency as the changes in pressure. What we perceive as very loud sounds are sound waves with very large amplitudes, meaning that the differences in pressure are very large. The larger changes in pressure could cause damage to the membrane by causing it to vibrate too violently.

### Review

1. Describe how sound is produce in a speaker, travels to your ear and how your ear converts these sound waves into sound in your brain.
2. The Indian instrument called a “sitar” uses two sets of strings, one above the other. Only one set of strings is played but both make sound. Research the sitar and explain briefly how this works.
3. A train, moving at some speed lower than the speed of sound, is equipped with a gun. The gun shoots a bullet forward at precisely the speed of sound, relative to the train. An observer watches some distance down the tracks, with the bullet headed towards him. Will the observer hear the sound of the bullet being fired before being struck by the bullet? Explain.
4. The speed of sound v\begin{align*}v\end{align*} in air is approximately 331.4 m/s+0.6 T\begin{align*}331.4 \ m/s + 0.6 \ T\end{align*}, where T\begin{align*}T\end{align*} is the temperature of the air in Celsius. The speed of light c\begin{align*}c\end{align*} is 300,000 km/sec, which means it travels from one place to another on Earth more or less instantaneously. Let’s say on a cool night (air temperature 10\begin{align*}10^\circ\end{align*} Celsius) you see lightning flash and then hear the thunder rumble five seconds later. How far away (in km) did the lightning strike?

1. The sound from a speaker travels in the form of compression waves through the air and is channeled into your ear and onto your eardrum. This moves hairs in the inner ear that deliver electric pulses to your auditory nerve which your brain interprets as sound.
2. When one set of strings on the sitar is plucked it vibrates a set of strings called the sympathetic strings which also vibrate and create a resonating sound.
3. Struck by bullet first.
4. 1.7 km

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