1. Child’s swing

2. Stereo speakers

3. Blade on a jigsaw

4. String on a guitar

2. Stereo speakers

3. Blade on a jigsaw

4. String on a guitar

Examples of everyday objects that exhibit SHM (4)

Yes, it’s momentarily zero as the mass passes through the equilibrium point

Is the acceleration of a SHO ever zero?

When the engine is running, the piston has a constant period and zero velocity at the top and bottom of its path

Why is the motion of the piston in a car engine SHM?

With a spring that has mass, the period will be larger and the frequency will be smaller

How does the frequency and period of a spring with mass compare to the frequency and period of a massless spring?

By doubling the amplitude

How could you double the maximum speed of a SHO?

The clock will run slower because g will be smaller, therefore making the period longer

If a pendulum clock is accurate at sea level, will it gain or lose time when taken to a high altitude? Why?

1). Pull the tire back a short distance and release it so that it oscillates as a pendulum in SHM with a small amplitude

2). Measure the period and calculate the length of the pendulum. The height, h, is the length l plus the height of the center of the tire to the ground.

2). Measure the period and calculate the length of the pendulum. The height, h, is the length l plus the height of the center of the tire to the ground.

A tire swing hanging from a branch reaches nearly to the ground. How could you estimate the height of the branch using only a stopwatch?

Displacement and velocity are in the same direction when the oscillator is moving away from equilibrium. Displacement and acceleration are never in the same direction.

For a SHO, when are the displacement and velocity vectors in the same direction? When are the displacement and acceleration vectors in the same direction?

Empty because the period of oscillation increases with increasing mass

Does a car bounce on its springs faster when it is empty or when it is fully loaded? Why?

The frequency will decrease because the moment of inertia will increase more than the added mass since the mass is located far from the axis of rotation. This causes the period to increase and the frequency to decrease.

A thin uniform rod of mass m is suspended from one end and oscillates with a frequency f. If a small sphere of mass 2m is attached to the other end, does the frequency increase or decrease?

single wave bump

pulse

When 2 or more waves pass through the same region of space at the same, the actual displacement is the vector (or algebraic) sum of the separate displacements.

Principle of superposition

It returns inverted of the end is fixed

It returns right side up if the end is free

It returns right side up if the end is free

How is a pulse reflected?

When the wave pulse reaches the boundary between the two sections, part of the pulse is reflected as an inversion and part is transmitted through the heavy section

For a cord which has a light section and a heavy section, describe its behavior

less energy is transmitted

As the second section of cord gets heavier…

The frequency. Therefore a lower speed=lower wavelength

What does not change in the transmission of a periodic wave across a cord with two different weights?

points of destructive interference

nodes

points of constructive interference

antinodes

Energy isn’t transmitted in a standing wave since the string is at rest at the nodes

How is energy transmitted in a standing wave?

Yes because a simple periodic wave travels through a medium, which must be in contact with or connected to the source for the wave to be generated

Is the frequency of a simple periodic wave equal to the frequency of its source? Why or why not?

1. Estimate the number of wave crests that pass a given point per second (frequency)

2. Estimate the distance between two successive crests (wavelength)

3. Multiply frequency by wavelength

2. Estimate the distance between two successive crests (wavelength)

3. Multiply frequency by wavelength

Describe how you could estimate the speed of water waves across the surface of a pond

The wave with the shorter wavelength will transmit 4 times the energy transmitted by the other wave since the energy transmitted by a wave depends on the wave speed and square of the frequency.

Two linear waves have the same amplitude and speed, and otherwise are identical, except one has half the wavelength of the other. Which transmits more energy? By what factor?

Yes because it will satisfy the wave equation

Will any function of (x-vt) represent a wave motion?

The frequency stays the same because the two sections of the cord must oscillate together.

When a sinusoidal wave crosses the boundary between two sections of cord, the frequency does not change. Explain why.

Shorter wavelength since the transmitted wave will travel more slowly in the heavier section of the cord.

If a sinusoidal wave on a two-section cord is inverted upon reflection, does the transmitted wave have a longer or shorter wavelength?

Yes, total energy is always conserved. The particles in the medium have both kinetic and potential energy.

Is energy always conserved when two waves interfere? Explain.

Yes, touching it at the nodes will not disturb the motion

If a string is vibrating as a standing wave in 3 segments, are there any places you could touch it with a knife blade without disturbing the motion?

No. The energy of the incident and reflected wave is distributed around the antinodes. The energy is a property of the wave as a whole.

When a standing wave exists on a string, the vibrations of incident and reflected waves cancel at the nodes. Does this mean that energy was destroyed? Explain.

20 Hz – 20,000 Hz

Audible range

ultrasonic

Frequencies above 20,000 Hz are…

Sound waves below the audible range

Infrasonic