Mastering Physics Solutions: Wave Notation

Mastering Physics Solutions: Wave Notation

On December 26, 2011, in Chapter 13: Vibrations and Waves, by Mastering Physics Solutions

Wave Notation

Part A = periodic
Part B = λ = v/f
Part C = decreases
Part D = radians
Part E = T = 1/f
Part F = ω = 2π * f

Solutions Below:

Part A

Traveling waves propagate with a fixed speed usually denoted as v (but sometimes c). The waves are called __________ if their waveform repeats every time interval T.

periodic

Part B

The fundamental relationship among frequency, wavelength, and velocity is

v = f / λ

Solve this equation to find an expression for the wavelength lambda.
Express your answer in terms of the velocity v and the frequency f.

λ = v/f

Part C

If the velocity of the wave remains constant, then as the frequency of the wave is increased, the wavelength __________.

decreases

Part D

The difference between the frequency f and the frequency ω is that f is measured in cycles per second or hertz (abbreviated Hz) whereas the units for omega are __________ per second.

radians

Part E

Find an expression for the period T of a wave in terms of other kinematic variables.
Express your answer in terms of any of f, v, ω, and simple constants such as pi.

T = 1/f

Part F

What is the relationship between ω and f?

ω is the angular frequency. Since a full circle has 2π radians, just multiply f by 2π:

ω = 2π*f

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