The period of vibration of a wave is the time it takes for one complete cycle, and it is inversely related to the frequency of the wave. The formula to calculate the period of a wave is:
Period (T) = 1 / Frequency (f)
To find the period of the sound wave in this scenario, we need to determine the frequency of the wave. The frequency can be calculated using the formula:
Frequency (f) = Speed (v) / Wavelength (λ)
Given that the speed of sound in air is 330 m/s and the wavelength is 1.65 m, we can substitute these values into the formula to calculate the frequency:
f = v / λ f = 330 m/s / 1.65 m f = 200 Hz
Now that we have the frequency, we can find the period using the formula mentioned earlier:
T = 1 / f T = 1 / 200 Hz T = 0.005 seconds
Therefore, the period of vibration for this sound wave in air is 0.005 seconds.