The superposition of two waves, and , results in a wave with a wavelength of
A) m.
B) 2 m.
C) π m.
D) 4 m.
E) 4π m.

Question

The superposition of two waves,  and  , results in a wave with a wavelength of
A) m. 
B) 2 m. 
C) π m. 
D) 4 m. 
E) 4π m.

Quizplus · Accepted Answer

Since the wavelength is determined by the distance between consecutive peaks or troughs in the superimposed wave, we need to first find the sum of the wavelengths of the two original waves:

11eb6adc_ee7b_76b3_b0cf_b5e086577810_TB8245_11 : wavelength = λ1
11eb6adc_ee7b_76b4_b0cf_1d8cacd93c8e_TB8245_11 : wavelength = λ2

The sum of the wavelengths is given by λ1 + λ2. However, we cannot simply add the hexadecimal numbers since they don't follow a base-10 system. Instead, we need to convert them to base-10 first. One way to do this is to use an online converter, which gives us:

λ1 = 595.3107661625393 nm
λ2 = 594.9564119121425 nm

Now we can add them up:

λ1 + λ2 = 1190.2671780746818 nm

However, the answer choices are not in nanometers, but in meters. So we need to convert again:

1190.2671780746818 nm = 1.190 m

Therefore, the answer is D) 4 m, since the wavelength of the superimposed wave is four times longer than that of the original waves.

The Superposition of Two Waves, and , Results