Question

As Section 27.5 discusses, sound waves diffract or bend around the edges of a doorway. Larger wavelengths diffract more than smaller wavelengths. (a) The speed of sound is 343 m/s. With what speed would a 57.0 kg person have to move through a doorway to diffract to the same extent as a 146 Hz bass tone? (b) At the speed calculated in part (a), how long in years (365.25 days) would it take the person to move a distance of one meter?

Answer 1

(a)
λ(sound)= λ1
λ (person)= λ2
λ(sound)= λ (person)
λ1= λ2
λ1=v/f=343/146=2.35 m.
λ2=h/p=h/(m•v2)
v2=h/(m• λ2)= h/(m• λ1)=
=(6.63•10^-34)/57•2.35 =4.95•10^-36 m/s.

(b) t=s/v=1/4.95•10^-36=
=2.02•10^35 s=6.4•10^27 years