The relationship between wavelength (λ), speed of sound (v), and period (T) is given by the formula:
v = λ * f
where: v = speed of sound in air (330 m/s) λ = wavelength of the sound wave (1.65 m) f = frequency of the sound wave (to be determined) T = period of vibration (to be determined)
We can rearrange the formula to solve for the frequency (f):
f = v / λ
Now, let's plug in the values:
f = 330 m/s / 1.65 m f = 200 Hz
The frequency (f) of the sound wave is 200 Hz, which means it completes 200 vibrations per second. The period (T) is the reciprocal of frequency:
T = 1 / f T = 1 / 200 Hz T = 0.005 seconds
So, the period of vibration of the sound wave is 0.005 seconds.