Two motors in a factory are running at slightly different rates.One runs at 825.0 rpm and the other at $786.0 \mathrm { rpm } \text {. }$ You hear the sound intensity increase and then decrease periodically due to wave interference.How long does it take between successive instances of the sound intensity increasing?
A)1.54 s
B)1.43 s
C)1.66 s
D)1.79 s

Question

Quizplus · Accepted Answer

To find the time between successive instances of sound intensity increasing, calculate the beat frequency, which is the difference in frequencies of the two motors: $825.0 \mathrm{rpm} - 786.0 \mathrm{rpm} = 39.0 \mathrm{rpm}$. Convert rpm to Hz (revolutions per second) by dividing by 60: $39.0 \mathrm{rpm} / 60 = 0.65 \mathrm{Hz}$. The period, or time between successive beats, is the inverse of the beat frequency: $1 / 0.65 \mathrm{Hz} = 1.54 \mathrm{s}$.

Two Motors in a Factory Are Running at Slightly Different 786.0rpm. 786.0 \mathrm { rpm } \text {. }786.0rpm.

Two Motors in a Factory Are Running at Slightly Different $786.0 \mathrm { rpm } \text {. }$