Dispersion and beats Consider two waves f,(x, t)- Acos(k, x-ot) and f,(x, t)- Acos(k2x- co, t) that propagate through the same medium. Assume ΔΚ-ki-k2 is much smaller than ki and k2. we saw in Lecture 6 that the resulting wave can be written as a product of two traveling waves, one oscillating at high frequency /short wavelength and one wavelength. If the medium in which the waves propagate has a dispersion relation ω(k-ck2 where c is a constant, what approximately are the wave velocities of the high frequency and low frequency part of the resulting wave? Are they the same? Show your work, and use a sketch of ω ( k ) to explain your answer.

the design of a ski jumping suit involves a trade-off between giving the skiers lift to get higher jumps and ensuring the skier does not face a lot of drag before the jump itself. an expansive suit may to lift the skier higher, but at the same time, it will also increase the air resistance. higher air resistance as the skier goes down the slope limits the speed of the jump. a big suit also increases the risk of losing balance or control, especially if there's a strong gust of wind. while technologically enhanced suits a lot, clothing is not the only factor in a ski jumper’s success. gathering speed while skiing down the slope, ensuring good speed on the ramp, and maintaining good body posture and form in the air all contribute to a ski jumper's success.