the speed of a transverse wave on a string is 450 m/s while the wavelength is .18m. the amplitude of the wave is 2mm how much time is required for a particle of the string to move through a total distance of 1km
To find the time required for a particle of the string to move through a total distance of 1 km, we need to calculate the period of the wave.
The speed of a wave (v) is given by the product of its wavelength (λ) and frequency (f): v = λ * f.
The frequency (f) of a wave is the reciprocal of its period (T): f = 1 / T.
Rearranging the equation v = λ * f, we get:
f = v / λ.
Now we can find the frequency by substituting the given values:
f = 450 m/s / 0.18 m = 2500 Hz.
Since f = 1 / T, we can solve for the period (T):
T = 1 / f = 1 / 2500 Hz = 0.0004 s (or 4 x 10^-4 s).
To calculate the time required for a particle of the string to move through a total distance of 1 km, we divide the distance (1 km or 1000 m) by the speed (450 m/s):
Time = Distance / Speed = 1000 m / 450 m/s = 2.22 s.
Therefore, it takes approximately 2.22 seconds for a particle of the string to move through a total distance of 1 km.
To find the time required for a particle of the string to move through a total distance of 1 km, we need to calculate the period of the wave.
The period (T) of a wave can be found using the equation:
T = 1 / f
where f is the frequency of the wave.
The frequency of a wave can be determined using the equation:
f = v / λ
where v is the speed of the wave and λ is the wavelength.
Given:
Speed of the wave (v) = 450 m/s
Wavelength (λ) = 0.18 m
First, calculate the frequency of the wave:
f = 450 m/s / 0.18 m
f = 2500 Hz
Now, calculate the period of the wave:
T = 1 / 2500 Hz
T = 0.0004 s
To find the time required for a particle of the string to move through a total distance of 1 km, we need to divide the total distance by the speed of the wave:
Time = Distance / Speed
Total Distance = 1 km = 1000 m
Speed = 450 m/s
Time = 1000 m / 450 m/s
Time = 2.22 s
Therefore, it would take approximately 2.22 seconds for a particle of the string to move through a total distance of 1 km.