Question

Imagine that treble sounds could travel at 400 m/s, but bass sounds traveled at only 300 m/s. If sound actually behaved that way, and you were listening to a brass band from a distance of 120m, how much delay would you hear between trumpet and tuba notes when they begin a chord together?

Answer 1

Answer:

$\Delta t = 0.1s$

Explanation:

We need to calculate the difference between the times the waves from the bass sounds ($t_b$) and treble sounds ($t_t$) take to reach us, that is, $\Delta t = t_b-t_t$.

Since $v=\frac{d}{t}$, then $t=\frac{d}{v}$ and we can write:

$\Delta t = t_b-t_t=\frac{d}{v_b} - \frac{d}{v_t}=d(\frac{1}{v_b} - \frac{1}{v_t})=(120m)(\frac{1}{300m/s} - \frac{1}{400m/s})=0.1s$