Learning object #2
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A spy is running through a villain's castle and encounters two approaching lava waves of equal frequency, wavelength, and amplitude. The resultant wave has an amplitude that is 4/5 of the individual waves. The phase constant between the resultant wave and one of the original waves is calculated to be 2.319 radians. If the spy was in front of the first wave, which has a wavelength of 2m, there would be enough space between the waves for the spy to jump over the first wave and run between them, as the distance between wave crests is one wavelength.
Learning object #2
- 1. LO 5 A spy is running through an evil villain’s castle. The villain is known to be a flashy character and has strange features in his castle. At one point, the spy has a two lava waves moving closer to her from behind. Suppose that the waves are of the same frequency, wavelength, and amplitude. In addition, the resultant wave has 4/5 of the amplitude of the two waves. a) Find the phase constant between the resultant wave and of one of the waves (for this part assume, that the two waves are harmonic waves). b) If the spy was in front of the front wave, (the wavelengths are 2m and the amplitudes are 1m for these waves), would there be enough space in between for the spy to jump over the first wave and run in between them (perhaps she wanted to hide from prying eyes somewhere…)? Amplitude = A Frequency = F Wavelength = ƛ Amplitude = A Frequency = F Wavelength = ƛ
- 2. Solution: a) To solve this, we can use equation 14-37, so we have that 2𝐴𝑐𝑜𝑠 ( 𝜙 2 ) = 4𝐴 5 cos ( 𝜙 2 ) = 2 5 𝜙 2 = cos−1 ( 2 5 ) 𝜙 = 2 cos−1 ( 2 5 ) = 2.319 rad b) The distance between two wave crests is simply one wavelength (if the wavelengths of the original two waves are the same). Therefore, the distance between two crests is equal to ƛ. Logically, if the spy was very athletic, she could jump over the wave and have enough space to run in between them.