Final answer:
Using the Doppler effect formula for approaching sources, the frequency heard by the driver of the second engine before they pass each other with a source frequency of 540 Hz and speeds of 60 m/s towards each other, is approximately 771 Hz, which is rounded to 780 Hz. Therefore, the correct answer is (d) 780 Hz.
Step-by-step explanation:
To calculate the frequency heard by the driver of the second engine before they pass each other, we can use the Doppler effect. The Doppler effect describes the change in frequency or wavelength of a wave in relation to an observer moving relative to the source of the waves. Because the two engines are moving towards each other, we can use the Doppler effect formula for approaching sources:
f' = f (v + vo) / (v - vs)
Where:
f' is the observed frequency,
f is the source frequency (540 Hz),
v is the speed of sound (which we'll assume is approximately 340 m/s unless otherwise provided),
vo is the speed of the observer relative to the medium (60 m/s, since the drivers are approaching each other),
vs is the speed of the source relative to the medium (60 m/s, since they are approaching).
Substituting in the known values:
f' = 540 Hz (340 m/s + 60 m/s) / (340 m/s - 60 m/s)
f' = 540 Hz (400 m/s) / (280 m/s)
f' = 540 Hz x (10/7)
f' = 540 Hz x 1.4286
f' = 771.4 Hz
So the frequency heard by the driver of the second engine before they pass each other would be approximately 771 Hz, which is option (d) 780 Hz after rounding to the nearest whole number.