Answer to Question #198541 in Mechanics | Relativity for emanuel

Question

Teboho stands on the side of the freeway. Randall has just passed his traveling 44 m/s and he is traveling north. While Morena is headed towards him from the south at a speed of 60 m/s. Thabiso hoots his horn that has a frequency of about 400 Hz. If we consider the speed of sound in air as 340 m/s. Calculate the horn’s frequency that Randall is hearing.

Answer 1

Wavelength of sound:

$\lambda=v/f=340/400=0.85\ m$

Relative speed of Morena respect to Randall is:

$\Delta v=60-44=16\ m/s$

If the horn is with Morena, then sound moving from Morena to Randall with speed:

$v_1=v+\Delta v=340+16=356\ m/s$

So, the horn’s frequency that Randall is hearing:

$f_1=v_1/\lambda=356/0.85=419\ Hz$