Mechanical sinusoidal transverse wave

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Homework Help Overview

The problem involves a sinusoidal transverse wave traveling along a string, with parameters including string tension and linear density. The original poster seeks to determine various characteristics of the wave, such as amplitude, wavelength, wave speed, period, maximum transverse speed, and phase angle.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to convert units for linear density and apply the wave speed formula but questions the correctness of their calculations. They also express confusion regarding the concepts of amplitude and the distinction between wave speed and maximum transverse speed.

Discussion Status

Some participants suggest starting calculations in SI units before converting to desired units, which may provide clarity. The original poster later indicates they have resolved their understanding of wavelength, wave speed, and period, but still seeks clarification on amplitude.

Contextual Notes

The original poster's calculations are influenced by unit conversion challenges, and there is an ongoing exploration of the definitions and relationships between wave properties.

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[SOLVED] mechanical waves

Homework Statement


A sinusoidal transverse wave is traveling along a string in the negative direction of an x-axis. The figure shows a plot of the displacement as a function of position at time t=0; the y-intercept is 4.0m. The string tension is 6.8N, and its linear density is 47.22 g/m.

Find the amplitude (cm).
Find the wavelength (cm).
Find the wave speed (cm/s).
Find the period of the wave.
Find the maximum transverse speed of a particle in the string.
What is the phase angle in degrees?

Homework Equations





The Attempt at a Solution


So linear density is the mass per unit length. it's not in the units we want (kg/cm), so convert and get 4.722E-4 kg/cm.
wave speed = sqrt(T/wave length) = sqrt(6.8/4.722E-4), but this isn't the right answer. did i convert wrong?

also I'm having trouble finding the amplitude and wave length, probably for the same reason as above.
 

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it is better to start from meter and kg, since N is in terms of these SI units. after calculation, you can always convert back to cm to give answers.
 
ok, got that wavelength wave sped and period. what is the difference between wave speed and max transverse speed? also, I'm sure this is really obvious but i can't figure out the amplitude either
 
never mind i got it, thanks
 

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