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Chapter 16: Q35P (page 474)

Two sinusoidal waves of the same frequency travel in the same direction along a string. If,ym1=3.0cm,ym2=4.0cm.蠒1=0,and蠒2=蟺/2radwhat is the amplitude of the resultant wave?

Short Answer

Expert verified

The amplitude of the wave is 5.00 cm

Step by step solution

01

The given data

i) Amplitude of first wave,y1m=3.00cmor0.03m

ii) Amplitude of second wave,y2m=4.00cmor0.04m

iii) The first phase,蠒1=0

iv) The second phase,蠒1=蟺/2

02

Understanding the concept of phase

A phasor is a vector that rotates around its tail which is pivoted at the origin of a coordinate system. Herey1mandy2mrepresents the amplitude of the two waves andymrepresents the amplitude of the resultant wave.

03

Calculation of amplitude


The angle made by the phasor of two corresponding waves is 90掳. Using the Pythagorean Theorem we can write,

ym2=y1m2+y2m2=32+42=25ym=5.00cm

So that the resultant amplitude is 5.00cm

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