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Waves and Sound! A mass bouncing up and down on a spring produces what is called “periodic motion”. If we stuck a pen on the mass and slid a piece of paper past it at a constant speed, we would get the graph above!

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Waves and Sound!

A mass bouncing up and down on a spring produces what is called “periodic motion”. If we stuck a pen on the mass and slid a piece of paper past it at a constant speed, we would get the graph above!


The source of any wave is something that vibrates, be it a mass on a spring or the electrons in a piece of metal on an antenna.

The electrons on the top of this antenna vibrate 940,000 times per second in response to an electric current applied to them. This produces radio waves with a frequency of 940 KHz radio waves you could listen to with your car radio!


We describe waves mathematically with two related terms:

Frequency is the number of waves per second

Period is how many seconds between each wave

Frequency in cycles/second has the unit “Hertz”

1 Hz = 1 wave/second


Wave Velocity

All waves travel at some speed or velocity. Light, radio waves, microwaves and any “electromagnetic” waves travel at the speed of light 186,000 miles per second (3.0 x 108 m/s). Einstein’s theories tell us that nothing in the universe can travel faster than this….

Other waves, like sound and water waves, travel more slowly:

If the wavelength is 1m and it takes 1 second for a wave to pass, its v = 1m/s


Drawing Waves

We can show waves by drawing the “wave fronts”, which would look like the ripples spreading out from a rock dropped into a lake or lines of waves approaching the beach:


We can also draw waves with “Rays” which are perpendicular to the wave fronts:


A simple formula for the speed of a wave is:

Wave Speed = wavelength x frequency

In the case of electromagnetic waves, since the speed is constant, this means that as wavelength increases, the frequency must decrease!


Two Basic Types of Waves

LONGITUDINAL wave has wave travel along the direction the source vibrates. These are also called compressional waves

TRANSVERSE waves has vibration perpendicular to the wave direction.


Sound Waves are Longitudinal or compressional waves. Air is compressed in small areas and these move away from the source of compression

If you move a ping-pong paddle back and forth rapidly in a room filled with ping-pong balls, the balls will also vibrate

Sound Waves


Sound travels about 1000 ft/second (343 m/s), so if we look at fireworks from a distance of 2000 feet, it takes the sound 2 seconds to get to us, while the light is nearly instantaneous…


A loudspeaker produces sound by moving a paper cone back and forth in response to an electric current. This produces compressional waves


Reflection of Sound

Smooth surfaces will reflect sound waves, while soft or irregular surfaces will tend to absorb it. Reflected sound makes a room seem “full”.

Since the distance traveled by a reflected sound wave may be longer than the direct path, we may sense and echo when the reflected wave arrives


The speed of sound in air depends on temperature:

speed of sound (m/s) = 331.5 + 0.60 T(°C)

so if we have a change in temperature near the surface of the Earth, sound rays may be “bent” or Refracted up or down.


We also use sound energy in medical sciences – using very high frequency or ultrasonic sound, which does no damage to cells (unlike x-rays!)


Marine Mammals such as Dolphins and Whales,. Use adjustable ultrasound imaging for hunting and communication



Almost all solid objects have a “natural frequency” of vibration. A swing’s resonant frequency depends on the length of the ropes!

If you want to push a kid higher on a swing, you have to apply the force at the right “frequency” and at the right point in the wave cycle. A force applied then will make the swing move higher. The same force at some other time may have no effect!


The Tacoma Narrows Bridge was completed in 1940. It was nicknamed “Galloping Gertie” because it moved in the high winds (30 – 40 mph) common in that part of the country. It completely collapsed 4 months after it was opened!


Movie clip


Wave Interference

Waves also interfere with each other (just like people!). If the top of one waves combines with the top of another, it is called constructive interference and the resulting wave will be higher than either of the two which produced it.

The extreme opposite case is the top of one wave will combine with the trough or “bottom” of another wave, and the wave can disappear completely!


If you plug in your stereo system speakers incorrectly, they will be out of phase and the sound will actually cancel if you put the speakers close to each other!


We use this idea to our advantage to cancel out sounds in noisy places like factories or aircraft.

Sound canceling headphones


The Doppler Effect

The frequency of the sound you hear is just the number of waves which hit your ears per second:

More waves = higher frequency = you hear “higher” sound

If the source of the sound waves is moving toward you, the waves moving from it to you will be “squished” or compressed a little because of the movement toward you. If it’s moving away, the waves will be stretched out.

“Squished” together waves = closer together = higher frequency to you!

“Stretched out” waves = pulled apart = lower frequency to you!


Doppler Effect

Doppler applet

Sound effect