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What phase difference between two otherwise identical traveling waves, moving in the same direction along a stretched string, will result in the combined wave having an amplitude 1.40 times that of the common amplitude of the two combining waves

Answer :

lublana

Answer:

[tex]91.14^{\circ}[/tex]

Explanation:

Wave function form for wave 1

[tex]y_1(x,t)=y_msin(kx-\omega t)[/tex]

Wave function form for wave 2

[tex]y_2(x,t)=y_msin(kx-\omega t+\phi)[/tex]

Resultant wave function of two waves

[tex]Y(x,t)=y_1(x,t)+y_2(x,t)=y_msin(kx-\omega t)+y_msin(kx-\omega t+\phi)[/tex]

[tex]Y(x,t)=y_m(sin(kx-\omega t)+sin(kx-\omega t+\phi))[/tex]

[tex]Y(x,t)=2y_mcos\frac{\phi}{2}sin(kx-\omega t+\frac{\phi}{2})[/tex]

By using the formula

[tex]sinA+sinB=2sin\frac{A+B}{2}cos\frac{A-B}{2}[/tex]

According to question

[tex]1.4y_m=2y_mcos(\frac{\phi}{2})[/tex]

[tex]cos\frac{\phi}{2}=\frac{1.4}{2}=0.7[/tex]

[tex]\frac{\phi}{2}=45.57[/tex]

[tex]\phi=2\times 45.57[/tex]

[tex]\phi=91.14^{\circ}[/tex]

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