To calculate the number of waves produced by a tuning fork to reach a person 90 meters away, we can use the formula:
number of waves = distance / wavelength
The wavelength can be calculated using the formula:
wavelength = speed of sound / frequency
Given that the frequency of the tuning fork is 460 Hz and the speed of sound in air is 340 m/s, we can calculate the wavelength:
wavelength = 340 m/s / 460 Hz
wavelength ≈ 0.739 m
Now we can use the wavelength to calculate the number of waves:
number of waves = 90 m / 0.739 m
number of waves ≈ 121.77 waves
Since the number of waves cannot be a fraction, we round it to the nearest whole number. Therefore, the tuning fork would produce approximately 122 waves to reach a person 90 meters away.