a violin string emits sound of freqency 510Hz.how for will be the sound waves reach when string completes 250vibration?the velocity of sound is 340M/S.
period = T = 1/f = 1/510 second
distance in one period = 340(1/510)meters
distance in 250 periods =250*340/510
To determine how far the sound waves will reach when the string completes 250 vibrations, you need to first calculate the wavelength of the sound waves using the frequency provided. Here's how:
1. Convert the frequency from Hz to cycles per second (cps):
510 Hz = 510 cps
2. Calculate the wavelength of the sound waves:
Wavelength (λ) = Velocity (v) / Frequency (f)
Given:
Frequency (f) = 510 cps
Velocity (v) = 340 m/s
λ = v / f
λ = 340 m/s / 510 cps
As the speed of sound is given in meters per second and the frequency is given in cycles per second, the resulting wavelength will be in meters.
λ ≈ 0.667 m
Now that we have the wavelength, we can determine how far the sound waves will travel when the violin string completes 250 vibrations:
3. Calculate the distance traveled by the sound waves:
Distance (d) = Wavelength (λ) × Number of Vibrations (n)
Given:
Number of Vibrations (n) = 250
d = 0.667 m × 250
d ≈ 166.75 m
Therefore, when the string completes 250 vibrations, the sound waves emitted by the violin string will travel approximately 166.75 meters.