Types of Traveling Waves Transverse wave – the displacement of the wave is perpendicular to the motion of the wave Sine and cosine graphs Light waves (electromagnetic waves) Longitudinal wave – the displacement of the wave is parallel to the motion of the wave Sound waves

Transverse Wave Figure 16.1  A pulse traveling down a stretched rope. The shape of the pulse is approximately unchanged as it travels along the rope.

Longitudinal Wave

Closer look at a Transverse Wave Figure 16.5  A one-dimensional pulse traveling to the right with a speed v. (a) At t = 0, the shape of the pulse is given by y = f(x). (b) At some later time t, the shape remains unchanged and the vertical position of an element of the medium any point P is given by y = f(x – vt).

Plots of the position y vs. x plot – provides information about the wavelength of the wave y vs. t plot – provides information about the period of the motion of the wave Active Figure 16.8  (a) The wavelength  of a wave is the distance between adjacent crests or adjacent troughs. (b) The period T of a wave is the time interval required for the wave to travel one wavelength. At the Active Figures link at http://www.pse6.com, you can change the parameters to see the effect on the wave function.

Equations of Motion

Equations of Motion (cont.)

Properties of the string Linear mass density: Wave speed:

IMPORTANT There are two different velocities for a traveling transverse wave. The wave velocity, which is literally how fast the wave is moving to the left or to the right. The transverse velocity, which is how fast the wave (rope, string) is moving up and down.

Energy in a Traveling Wave

Sound Sound waves are Infrasonic – less than 20 Hz Longitudinal Pressure Waves Infrasonic – less than 20 Hz Audible – between 20 and 20,000 Hz Ultrasonic – greater than 20,000 Hz Frequency – tone Amplitude – volume

Sound waves are mechanical waves, which means the wave needs a medium to travel through. (This is why there is no sound in space, there is no air for the sound wave to propagate through) Sound waves are traveling pressure waves. They are packets of low and high pressure regions which are picked up by your eardrums and interpreted as sounds in your brain.

Figure 17. 1 Motion of a longitudinal pulse through a compressible gas Figure 17.1  Motion of a longitudinal pulse through a compressible gas. The compression (darker region) is produced by the moving piston.

Active Figure 17.2  A longitudinal wave propagating through a gas-filled tube. The source of the wave is an oscillating piston at the left. The high-pressure and low-pressure regions are colored darkly and lightly, respectively. At the Active Figures link at http://www.pse6.com, you can adjust the frequency of the piston.

Figure 17.3  (a) Displacement amplitude and (b) pressure amplitude versus position for a sinusoidal longitudinal wave.

Speed of Sound In air (at 20 oC) = 343 m/s In air (T in Kelvin)

Speed of Sound In a fluid or gas - depends on the density of the medium and the Bulk Modulus (ch. 9) In a solid - depends on the density of the medium and the Young’s Modulus (ch. 9)

Power in a sound wave Previously, we calculated the power (the rate of energy transfer) in a wave traveling on a string. In the same way, we can calculate the power in a sound wave as it propagates through a medium. Energy in one wavelength: Power in one wavelength:

Intensity of Sound Another important property of sound waves is the intensity. The intensity of a wave is defined as the rate at which energy flows through a surface area – the power per unit area.

Intensity of Sound (cont.) We can also write the intensity in terms of the pressure of the sound wave: This equation for intensity is more practical in experimental applications because r and v are properties of the medium, therefore they are easier to determine in an experiment than w and smax which are properties of the sound wave.

Decibel Level Io=1.0 x 10-12 W/m2 Because our hearing covers a frequency range of 20 - 20,000 Hz, it’s often easier to talk about sound intensity in terms of decibels (dB). Io=1.0 x 10-12 W/m2 (this is the reference intensity – the sound intensity at the threshold of hearing)

Figure 17.6 Approximate frequency and sound level ranges of various sources and that of normal human hearing, shown by the white area.

Spherical and Plane Waves Sound waves are spherical waves – they move away from a source in all directions. But if you’re close to the source, the waves look (and act) as though they’re plane waves.

Multiple Sources of Sound If there are two or more sound sources, the total intensity of the sound you hear is the sum of the intensity of each individual sound wave.

Doppler Effect Because sound waves are spherical waves, your position and motion (relative to the source of the sound) will affect what you hear. This effect is called the Doppler Effect. If neither the source nor the observer are moving, then the sound heard by the observer will not be altered. But if either the source or the observer (or both) are moving relative to each other, then there will be a Doppler shift in the frequency (tone) of the sound.