The superposition of two waves, $$y _ { 1 } = \left( 2 \times 10 ^ { - 8 } \mathrm {~m} \right) \sin \left[ \pi \left( \frac { x } { 2 \mathrm {~m} } - \frac { 170 } { \mathrm {~s} } t \right) \right]$$ and $$y _ { 2 } = \left( 2 \times 10 ^ { - 8 } \mathrm {~m} \right) \sin \left[ \pi \left( \frac { x } { 2 \mathrm {~m} } - \frac { 170 } { \mathrm {~s} } t - \frac { 1 } { 2 } \right) \right]$$ , results in a wave with a wavelength of
A) $\frac { \pi } { 2 }$ m.
B)2 m.
C) $\pi$ m.
D)4 m.
E)4 $\pi$ m.

Question

The superposition of two waves, $$y _ { 1 } = \left( 2 \times 10 ^ { - 8 } \mathrm {~m} \right) \sin \left[ \pi \left( \frac { x } { 2 \mathrm {~m} } - \frac { 170 } { \mathrm {~s} } t \right) \right]$$ and $$y _ { 2 } = \left( 2 \times 10 ^ { - 8 } \mathrm {~m} \right) \sin \left[ \pi \left( \frac { x } { 2 \mathrm {~m} } - \frac { 170 } { \mathrm {~s} } t - \frac { 1 } { 2 } \right) \right]$$ , results in a wave with a wavelength of
A) $\frac { \pi } { 2 }$ m.
B)2 m.
C) $\pi$  m.
D)4 m.
E)4 $\pi$ m.

Quizplus · Accepted Answer

The wavelength of the resulting wave can be found by using the formula λ = v/f, where v is the velocity of the wave and f is the frequency. Since the two waves have the same frequency and velocity, the resulting wave will also have the same frequency and velocity. Therefore, the wavelength of the resulting wave will be equal to twice the wavelength of either of the two original waves.

Given that the wavelength of the first wave is 11ea99f6_d724_0d18_8bb6_1193b9e983d5_TB5764_00_TB5764_00_TB5764_00_TB5764_00_TB5764_00_TB5764_00_TB5764_00_TB5764_00 m, the wavelength of the resulting wave will be:

2 x 11ea99f6_d724_0d18_8bb6_1193b9e983d5_TB5764_00_TB5764_00_TB5764_00_TB5764_00_TB5764_00_TB5764_00_TB5764_00_TB5764_00 = 4 m.

Therefore, the correct answer is D.

The Superposition of Two Waves And , Results in a Wave with a Wavelength of A)

The Superposition of Two Waves And , Results in a Wave with a Wavelength of
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