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Physics 101: Lecture 32Waves and Sound

- Today’s lecture will cover Textbook Sections16.1 - 16.5
- Review: Simple Harmonic Motion (Chapter 10)

Please check all of the entries in your grade book to make sure none of the grades are missing or messed up. Please contact your TA in case you have questions concerning your homework grades.

Review: Simple Harmonic Motion

- The position x of an object moving in simple harmonic motion as a function of time has the following form:

x = A cos (wt)

i.e. the object periodically moves back and forth between

the amplitudes x=+A and x=–A.

The time it takes for the object to make one full cycle is

the period T=2p/w=1/f, where f is the frequency of the

motion.

Thus, the angular speed in terms of T and f reads

w = 2p/T and w = 2 p f

- Nature of waves:
- A wave is a traveling disturbance that transports energy from place to place.
- There are two basic types of waves: transverse and longitudinal.
- Transverse: the disturbance travels perpendicular to the

direction of travel of the wave.

- Longitudinal: the disturbance occurs parallel to the line of

travel of the wave.

- Examples:
- Longitudinal: Sound waves (e.g. air moves back & forth)
- Transverse: Light waves(electromagnetic waves, i.e. electric and magnetic disturbances)

The source of the wave, i.e. the disturbance, moves continuously in

simple harmonic motion, generating an entire wave, where each

part of the wave also performs a simple harmonic motion.

Transverse: The medium oscillates perpendicular to the direction the wave is moving.

- Water waves (also have a longitudinal component)

- Longitudinal: The medium oscillates in the same direction as the wave is moving
- Sound

Types of Waves

Wavelength: The distance between identical points on the wave.

- Amplitude: The maximum displacement A of a point on the wave.

Wavelength

Amplitude A

A

Wave Properties

Period: The time T for a point on the wave to undergo one complete oscillation.

- Speed: The wave moves one wavelength in one period T so its speed is v = / T.

Wave Properties...

Wave Properties...

- The speed of a wave is a constantthat depends only on the medium,

not on the amplitude, wavelength or period:

and T are related !

- = v T or = 2 v / (sinceT = 2 / or = v / f (since T = 1/ f )
- Recallf = cycles/sec or revolutions/sec

= 2f

Is the speed of a wave particle the same as the speed of the wave ?

No. Wave particle performs simple harmonic motion: v=A w sin wt.

Concept Question

Suppose a periodic wave moves through some medium. If the period of the wave is increased, what happens to the wavelength of the wave assuming the speed of the wave remains the same?

1. The wavelength increases

2. The wavelength remains the same

3. The wavelength decreases

Concept Question

The speed of sound in air is a bit over 300 m/s, and the speed of light in air is about 300,000,000 m/s. Suppose we make a sound wave and a light wave that both have a wavelength of 3 meters. What is the ratio of the frequency of the light wave to that of the sound wave?

1. About 1,000,000.

2. About 1,000.

3. About 0.000001.

f = v/

fL/fS = vL/vS = 1,000,000

Transverse Waves on a String (e.g. Guitar)

Speed:

T=Tension : the greater the tension in the string the greater

the pulling force the particles exert on each other

and the faster the wave travels.

m=mass/length of the string = m/L= linear density of the spring:

the smaller the mass the greater the acceleration for

the same pulling force and the faster the wave travels.

correct

Concept QuestionA rope of mass M and length L hangs from the ceiling with nothing attached to the bottom (see picture). Suppose you start a transverse wave at the bottom end of the rope by jigglingit a bit. As this wave travels up the rope its speed will:

1. Increase

2. Decrease

3. Stay the same

the tension gets greater as you goup

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