A violin string is vibrating at a frequency of 440 Hz. How many vibrations does the string make while its sound travels 200 m in air?
what is the speed of sound in air? If it is v m/s, then
200/v * 440 = ____
To find out how many vibrations the string makes while its sound travels 200 m in air, we need to use the formula that relates frequency, velocity, and wavelength.
The velocity of sound in air is approximately 343 meters per second at room temperature. So, we can calculate the wavelength (λ) of the sound by dividing the velocity (v) by the frequency (f):
λ = v / f
Substituting the given values:
λ = 343 m/s / 440 Hz = 0.7795 m
Now, to calculate the number of vibrations the string makes while the sound travels 200 meters, we can divide the distance traveled by the wavelength:
Number of vibrations = distance traveled / wavelength
Number of vibrations = 200 m / 0.7795 m ≈ 256.46
Therefore, the string would make approximately 256 vibrations while its sound travels 200 meters in air.