ENVS 1200 Chapter Notes - Chapter 2: Sine Wave, Nanosecond, Radio Wave

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amberdolphin86

13 May 2018

School

York University

Department

Environmental Studies

Course

ENVS 1200

Professor

Anders Sandberg

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ENVS 1200 Chapter 2 Notes – Summary

Introduction

• The period of a sine wave is the amount of time it takes to trace out one complete cycle

of the wave.

• Thus, the frequency, f, is defined as the number of periods per second, or

mathematically, f = 1/T or conversely, T = 1/f where T is the period, measured in

seconds.

• The amplitude and period are shown in the diagram.

• For this particular sine wave, the period is one-quarter second, and the frequency is four

cycles per second, or more commonly, 4 Hertz.

• Hertz, usually abbreviated Hz, is the unit used to measure frequency.

• One Hertz corresponds to one cycle per second.

• Note from the diagram, also, that since the sine wave is symmetric about the center

axis, its amplitude is measured from the center axis to either peak, not from negative

peak to positive peak.

• Sometimes it is useful to view a sine wave from a slightly different perspective

• What is the physical length of a sine wave that is traveling in space at the speed of light?

• This parameter is known as the wavelength of the sine wave.

• It is usually desigated y the Greek letter lada λ.

• It should be apparent to you that at a higher frequency the wavelength of a single sine

wave will be shorter because the waveform will not have time to travel as far before the

wave is complete.

• In fact, the wavelength of a sine wave signal is inversely related to its frequency as

follows: λ = C/F where  is the speed of light.

• For calculation purposes, the speed of light in a vacuum is approximately 300 million

meters per second or one foot per nanosecond.

• This latter figure might surprise you.

• You may be unconsciously aware of one interesting application of this formula

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Related Questions

Lets try this again, I was told to post this here because it'sapparently too advanced for alg-precalc.

When sound waves travel through a solid, a liquid, or a gas, themolecules of the medium vibrate in the direction of the motion ofthe sound wave. The frequency, f, of a sound wave is measured innumber of vibrations in a second. The unit of measure is hertz. Onehertz (Hz) is one vibration per second. The human ear can hear arange of frequencies from about 20 Hz to about 20,000 Hz.Frequency, wavelength, C, and speed, v, of a sound wave are relatedby the formula, v = fC.

The price of soundproofing a room depends on the frequency of thesound. A contractor used this formula to quote a price to John tosoundproof a room: P = 2491.5f, where P represents the price. TheSmith home has 7 rooms How much will it cost Miguel to soundproofall the rooms in his home?

$ 1152.44
$1534.76
$2685.84
$1918.45

Solve ALL

Guided Project 66: Traveling waves Topics and skills: Functions of two variables, partial derivative, graphing The word wave elicits images of water waves rolling in beach. However, wave is used to describe any disturbance that propagates through a medium. So the word includes water waves, sound waves, electromagnetic waves (light waves and cell phone signals), seismic waves, and waves in traffic on a crowded highway, In this project, we examine some of the fundamental mathematical properties of waves. 1. Consider the function z= f(x, t) = 3 sin (pi x- 2 pi t). It is easy to graph this function (Figure 1) and indeed we waves. But this graph really doesn't explain how and why waves propagate. To interpret the graph suppose that x and t represent distance (measured in meters) and time (measured in seconds), respectively. Specifically, the x-axis is the direction in which the wave propagates and z represents the height of the surface of the wave at a particular location and time. The maximum values of z correspond to crests of the wave and the minimum values of z correspond to troughs of the wave. What are the minimum and maximum values of z? 2. Now imagine that you are sitting on the Jt-axis, say at x = 2, watching the wave pass. Set x = 2 in z = f(x, t) and graph z = z(2, t) on the interval 0 t 2. Explain how z varies on 0 t 2. How many times do you observe a crest of the wave pass? The time that elapses between passing crests is the period of the wave. How many wave crests pass per second? The number of wave crests that pass per second passes is the frequency of the wave, usually measured in cycles per second. Instead of freezing x as we did in Step 2, we can also freeze t. Suppose you take a snapshot of the wave at t = 1. Set t = 1 in z = f(x, t) and graph z =f(x, 1) on the interval 0 x 4. Explain how z varies on 0 x 4. What is the distance between crests? The distance between crests is called the wavelength of the wave. How far does the crest of the wave travel in one second of time? What is the speed of the wave?

Good Vibes: Introduction to Oscillations

The conditions that lead to simple harmonic motion are as follows:

There must be a position of stable equilibrium.

There must be a restoring force acting on the oscillating object. The direction of this force must always point toward the equilibrium, and its magnitude must be directly proportional to the magnitude of the object's displacement from its equilibrium position. Mathematically, the restoring force F⃗ is given by ⃗, where is the displacement from equilibrium and k is a constant that depends on the properties of the oscillating system.

The resistive forces in the system must be reasonably small.

Consider a block of mass m attached to a spring with force constant k, as shown in the figure(Figure 1) . The spring can be either stretched or compressed. The block slides on a frictionless horizontal surface, as shown. When the spring is relaxed, the block is located at x=0. If the block is pulled to the right a distance A and then released, A will be the amplitude of the resulting oscillations.

Assume that the mechanical energy of the block-spring system remains unchanged in the subsequent motion of the block.

Part A

After the block is released from x=A, it will

(a) remain at rest

(b) move to the left until it reaches equilibrium and stop there.

(d) move to the left until it reaches x=−A and then begin to move to the right.

The time it takes the block to complete one cycle is called the period. Usually, the period is denoted T and is measured in seconds.

The frequency, denoted f, is the number of cycles that are completed per unit of time: f=1/T. In SI units, f is measured in inverse seconds, or hertz (Hz).

Part B

If the period is doubled, the frequency is

(a) unchanged

(b) doubled

Part C

An oscillating object takes 0.10 s to complete one cycle; that is, its period is 0.10 s. What is its frequency f?

Express your answer in hertz.

Part D

If the frequency is 40 Hz, what is the period T?

Express your answer in seconds.

The following questions refer to the figure (Figure 2) that graphically depicts the oscillations of the block on the spring.

Note that the vertical axis represents the x-coordinate of the oscillating object, and the horizontal axis represents time.

Part E

Which points on the x-axis are located at a distance A from the equilibrium position?

(a) R only

(b) Q only

Part F

Suppose that the period is T. Which of the following points on the t-axis are separated by the time interval T?

(a) K and L

(b) K and M

(d) L and N

(e) M and P

Now assume for the remaining Parts G - J, that the x coordinate of point R is 0.12 m and the t coordinate of point K is 0.0050 s.

Part G

What is the period T?

Express your answer in seconds.

Part H

How much time t does the block take to travel from the point of maximum displacement to the opposite point of maximum displacement?

Express your answer in seconds.

Part I

What distance d does the object cover during one period of oscillation?

Express your answer in meters.

Part J

What distance d does the object cover between the moments labeled K and N on the graph?

Express your answer in meters.

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ENVS 1200 Chapter Notes - Chapter 2: Sine Wave, Nanosecond, Radio Wave

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