Final answer:
To find the period of a sound wave with a 10 m wavelength, use the speed of sound (343 m/s) to determine the frequency, then invert the frequency to obtain the period, which is approximately 0.029 seconds.
Step-by-step explanation:
To solve for the period of a sound wave with a given wavelength, we need to use the formula for the wave speed (v), which is the product of the frequency (f) and the wavelength (λ):
v = f × λ
The speed of sound in room temperature air is about 343 m/s. Given the wavelength (λ) of 10 m, we want to find the period (T), which is the inverse of the frequency (T = 1/f), so first we need to find the frequency using the formula:
f = v / λ
Substituting the given values:
f = 343 m/s / 10 m
f = 34.3 Hz
Now calculating the period (T):
T = 1 / f
T = 1 / 34.3 Hz
T ≈ 0.029 s
Therefore, the period of the sound wave is approximately 0.029 seconds.