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6) In the figure below are shown graphs which could represent properties of pulses on a stretched string. For the situation and the properties (a) - (e) below, select which graph provides the best representation of the given property. If none of the graphs are correct, write "none". 

Two pulses are started on a stretched string. At time t=t₀ , an upward pulse is started on the right that moves to the left. At the same instant, a downward pulse is started on the left that moves to the right. At t₀ their peaks are separated by a distance 2s. The distance between the pulses is much larger than their individual widths. The pulses move on the string with a speed v₀ . The scales in the graphs are arbitrary and not necessarily the same. 

(a) Which graph best represents the appearance of the string at time t₀ ?
(b) Which graph best represents the appearance of the string at a time t₀  + s / v₀?
(c) Which graph best represents the appearance of the string at a time t₀  + 2s / v₀?
(d) Which graph best represents the velocity of the string at a time t₀  + s / v₀?
(e) Which graph best represents the appearance of the string at a time t₀  + s / v₀ + e where e is small compared to s/v₀ ? 

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Page last modified October 30, 2002: O21