Chapter 16: Q35P (page 474)

Two sinusoidal waves of the same frequency travel in the same direction along a string. If, $y_{m 1} = 3.0 cm, y_{m 2} = 4.0 cm . ϕ_{1} = 0, and ϕ_{2} = π / 2 rad$ what is the amplitude of the resultant wave?

Short Answer

Expert verified

The amplitude of the wave is 5.00 cm

Step by step solution

The given data

i) Amplitude of first wave, $y_{1 m} = 3.00 cm or 0.03 m$

ii) Amplitude of second wave, $y_{2 m} = 4.00 cm or 0.04 m$

iii) The first phase, $ϕ_{1} = 0$

iv) The second phase, $ϕ_{1} = π / 2$

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. Here $y_{1 m} and y_{2 m}$ represents the amplitude of the two waves and $y_{m}$ represents the amplitude of the resultant wave.

Calculation of amplitude

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

$y_{m}^{2} = y_{1 m}^{2} + y_{2 m}^{2} = 3^{2} + 4^{2} = 25 y_{m} = 5.00 cm$

So that the resultant amplitude is $5.00 cm$

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Two sinusoidal waves of the same frequency travel in the same direction along a string. If, $y_{m 1} = 3.0 cm, y_{m 2} = 4.0 cm . ϕ_{1} = 0, and ϕ_{2} = π / 2 rad$ what is the amplitude of the resultant wave?

Short Answer

Step by step solution

The given data

Understanding the concept of phase

Calculation of amplitude

One App. One Place for Learning.

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Two sinusoidal waves of the same frequency travel in the same direction along a string. If,ym1=3.0cm,ym2=4.0cm.ϕ1=0,andϕ2=π/2radwhat is the amplitude of the resultant wave?

Short Answer

Step by step solution

The given data

Understanding the concept of phase

Calculation of amplitude

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Physics Textbooks

Translational Dynamics

Engineering Physics

Solid State Physics

Geometrical and Physical Optics

Physical Quantities And Units

Electricity and Magnetism

Study anywhere. Anytime. Across all devices.

Two sinusoidal waves of the same frequency travel in the same direction along a string. If, $y_{m 1} = 3.0 cm, y_{m 2} = 4.0 cm . ϕ_{1} = 0, and ϕ_{2} = π / 2 rad$ what is the amplitude of the resultant wave?