To calculate the distance traveled by a sound wave in the time taken to produce a certain number of waves, we need to use the wave speed formula:
Wave speed = Frequency × Wavelength
Given that the frequency is 200 Hz (or 200 cycles per second) and the wavelength is 150 cm (or 1.5 meters), we can calculate the wave speed:
Wave speed = 200 Hz × 1.5 m = 300 m/s
The wave speed represents the distance traveled by the sound wave in one second. To find the distance traveled in the time taken to produce 150 waves, we divide the total time by the period of one wave:
Time taken for 150 waves = (150 waves) / (200 Hz) = 0.75 seconds
Finally, we can calculate the distance traveled by multiplying the time taken by the wave speed:
Distance = Wave speed × Time taken Distance = 300 m/s × 0.75 s = 225 meters
Therefore, the sound wave would have traveled a distance of 225 meters in the time taken to produce 150 waves.