PHYS 1114: Physics I

Lecture 11: Waves, Sound, & Light

Professor Kenny L. Tapp

Waves

• Waves&are&disturbances&(energy)&that&propagate&(move)&

• Waves&involve&a&oscilla8on&of&something&about&an&equilibrium&point– Pendulum(swinging

– Block(and(Spring(oscilla5ng

– Air(Molecules

– Electric(and(Magne5c(fields

Displacement (x) is the directed distance of the object from equilibrium.

Amplitude (A) is the maximum displacement.Period (T) is the time for one full cycle.

Frequency (f) is the number of full cycles per second.

Simple Harmonic Motion

SI unit of frequency: hertz, Hz

1 Hz = 1 cycle/second

A wave pulse is a disturbance that propagates through a

medium. It transfers energy without transferring matter; the energy is a combination

of kinetic and potential energy.

Wave Motion

• Longitudinal

• Transverse

Wave Motion

–&par8cle’s&oscilla8on&is&perpendicular&to&the&pulse’s&mo8on.&Examples:&Light&waves,&sin&waves,&S&waves&in&earthquakes

–&par8cle’s&oscilla8on&is&parallel&to&the&pulse’s&mo8on.Examples:&Sound&waves,&P&waves&in&earthquakes

• Longitudinal

• Transverse

Wave Motion

‣ Parts • Crest • Trough

‣ Measurements of a wave• Wave height – the distance between a trough and a

crest • Wavelength – the horizontal distance between

successive crests (or troughs)• Wave period – the time interval for one full wave to

pass a fixed position

Wave Motion

Relationship between wave speed, wavelength, period, and frequency:

Wave Motion

Wavelength & Frequency

Long wavelengthLow frequency

Short wavelengthHigh frequency

Wavelength&increases&=&Frequency&decreases

Quick Question 1A car driving along a highway at a speed of 23 m/s strays onto the shoulder. Evenly spaced parallel grooves called “rumble strips” are carved into the pavement of the shoulder. Rolling over the rumble strips causes the car’s wheels to oscillate up and down at a frequency of 82 Hz. How far apart are the centers of adjacent rumble-strip grooves?

Quick Question 1 ... We can think of the rumble strips as a wave carved

into the surface of the road. The wave is stationary relative to the road, but its speed v relative to the car is equal to the car’s speed v relative to the road. The frequency f of the wave is equal to the frequency of the wheel vibrations caused by the wave. The distance between the centers of adjacent grooves, then, is the wavelength of the rumble-strip wave.

Quick Question 2Tsunamis are fast-moving waves often generated by underwater earthquakes. In the deep ocean their amplitude is barely noticeable, but upon reaching shore, they can rise up to the astonishing height of a six-story building. One tsunami, generated off the Aleutian islands in Alaska, had a wavelength of 750 km and traveled a distance of 3700 km in 5.3 h. (a) What was the speed (in m/s) of the wave? For reference, the speed of a 747 jetliner is about 250 m/s. Find the wave’s (b) frequency and (c) period.

Quick Question 2 ...

(a)

(b)

(c)

!

This is an illustration of interference, using the principle of superposition. The displacement of any point on the rope is the sum of

the individual displacements:

Wave Properties

If the combined wave is larger than the individual ones, the interference is constructive; if smaller, it is destructive.

Wave Properties Waves in Oklahoma

Waves in Oklahoma Waves in Oklahoma

• Create or observe waves in a fluid. Take a picture of the waves and label these parts of the wave that you photographed: crest, trough, wavelength, wave height.

• Additionally, take the following measurements of the waves that you are observing or creating and include that information on your picture: wavelength, wave height, wave period, wave frequency.

• Also observe and document an example of wave interference.

• You may work as a team to accomplish this, but you will need to document who you worked with on your individual submission.

19

Waves in Oklahoma Standing Waves & Resonance

Standing waves don't go anywhere, but they do have regions where the disturbance of the wave is quite small, almost zero. These locations are called nodes. There are also regions where the disturbance is quite intense, greater than anywhere else in the medium, called antinodes.

When an integral number of half-wavelengths fit on the

rope, the frequency is called the resonant frequency.

Standing Waves & Resonance

A standing wave is a pattern which results from the

interference of two or more waves traveling in the same

medium. Nodes

Antinodes

When a string stretched between two fixed points is plucked it vibrates in

what is know as its fundamental mode of vibration (aka the first harmonic).

Natural frequencies for a stretched string:

• For a given harmonic, the wavelength, λ, may be written: λ = 2l , where l is the length of the string between the fixed endpoints and n is the number of loops in the string.

• The velocity of a wave may be expressed as the product of its wavelength and frequency: v = λf . The velocity of a wave is the speed at which a fixed point on the wave propagates through the medium in which the wave is traveling. For a wave traveling down a

string the velocity may be expressed: v = 2lf .

Standing Waves & Resonance

n

n

Natural wavelengths can be varied by:

+ varying the length of a string, such as in a piano or harp;

+ varying the mass per unit length of a string, as in a guitar;

+ varying the tension, which is done for fine tuning.Driving a system at its natural frequency produces resonance.

Standing Waves & Resonance

The wave speed is given by

where FT is the tension and µ is the mass per unit length.

Quick Question 3

• A 50 m long string has a mass of 0.010 kg. A 2.0 m segment of the string is fixed at both ends and when a tension of 20 N is applied to the string, three loops are produced. What is the frequency of the standing wave?

Infrasonic waves have frequencies too low for human ears. They are

produced by earthquakes and other natural phenomena; elephants and cows can hear certain frequencies.

Ultrasonic waves are too high in frequency for human ears. Dogs, cats, and bats can hear higher frequencies.

Sound Waves

Speed of sound in a solid:

Y is Young’s modulus and ρ is the density.

Speed of sound in a liquid:

B is the bulk modulus.

The Speed of Sound

Speed of sound in dry air:

The$Speed$of$Sound:$$FIREWORKS

July 4, 201110:05pm

Air Temperature (Celsius)

v = 331 + (0.6Tc) = 331 + (0.6)(30) = 349 m/s

The$Speed$of$Sound:$$FIREWORKS

The$Speed$of$Sound:$$FIREWORKS

Determine the distance that Prof. Tapp was watching the fireworks

from on July 4, 2011.

Vsound = d / t

Quick Question 4

• The speed of an ultrasonic sound of frequency 45 kHz in air is 342 m/s.

(a) What is the air temperature?

(b) What is the wavelength of the sound wave?

Sound intensity is measured on a logarithmic scale, in decibels:

Sound$Intensity$and$Sound$Intensity$Level

We perceive sound intensity as loudness; the minimum detectable sound has an intensity of about 1.0 × 10–12 W/m2, and the threshold of pain occurs at an intensity of about 1.0 W/m2.

A doubling of loudness corresponds to an increase in intensity of about a factor of 10.

Visible light occupies only a tiny sliver of

the full spectrum.

ENERGY

As a car or train horn approaches you and then passes by, the pitch of the sound first rises and then falls. This is called the Doppler effect.

The Doppler Effect The Doppler Effect

The Doppler Effect

The Doppler Effect

Quick Question 5• A cop car drives at 30 m/s toward the scene of a crime, with its siren

blaring at a frequency of 2000 Hz. At what frequency do people hear the siren as it approaches? At what frequency do they hear it as it passes? The speed of sound in the air is 343 m/s.

Moving Toward:

Moving Away:

Quick Question 5...

Moving Toward:

Moving Away: