The speed of a transverse wave on a string is 457 m/s, while the wavelength is 0.228 m. The amplitude of the wave is 2.05 mm. How much time is required for a particle of the string to move through a total distance of 1.34 km?
To find the time required for a particle of the string to move through a total distance of 1.34 km, we can use the formula:
Time = Distance / Velocity
First, let's convert the distance from kilometers to meters:
1.34 km = 1.34 * 1000 = 1340 m
Now, let's calculate the time required using the given velocity:
Time = 1340 m / 457 m/s
Calculating this, we find:
Time ≈ 2.93 seconds
Therefore, it would take approximately 2.93 seconds for a particle of the string to move through a total distance of 1.34 km.
To solve this problem, we need to use the formula for the speed of the wave:
Speed = Frequency × Wavelength
We can rearrange the formula to solve for the frequency:
Frequency = Speed / Wavelength
Given that the speed of the wave is 457 m/s and the wavelength is 0.228 m, we can calculate the frequency as:
Frequency = 457 m/s / 0.228 m
Now, we can use the formula for the period of a wave to calculate the time required for a particle of the string to move through a total distance of 1.34 km. The period (T) of a wave is the reciprocal of the frequency (f), which is:
Period = 1 / Frequency
To find the time (t) required for a particle to move through a distance (d), we can use the formula:
t = d / v
where v is the velocity of the particle.
In this case, the distance is 1.34 km, which we need to convert to meters:
1.34 km = 1.34 × 1000 m = 1340 m
Now, we can substitute the values into the formula to calculate the time:
t = 1340 m / (457 m/s / 0.228 m)
Simplifying the equation, we get:
t = 1340 m / (2002.63 Hz)
Finally, we can calculate the time:
t ≈ 0.67 s
Therefore, it would take approximately 0.67 seconds for a particle of the string to move through a total distance of 1.34 km.