The tine of a tuning fork, when struck, has an amplitude of 0.13 cm. If the frequency of the fork is 200 Hz, what total distance will the tine travel in 1.0 minute?

where does the 4 come from?

Tuning fork has frequancy f= 200 Hz +> it makes 200 oscollations during 1 s.

Since 1 min=60 s, it makes 200•60=12000 oscillations/min.
Each oscillation = 4A=4•0.13 cm=4•0.0013 m=0.0052 m.
Therefore,
s=0.0052•12000=62.4 m.

the 4 comes from the amount of times .13 is moved on a transverse wave. It moves up(+.13), moves down to line (+.13), moves down(+.13, )moves back up(.13). = 4*.13

Well, if the tine of the tuning fork has an amplitude of 0.13 cm and a frequency of 200 Hz, it's certainly getting quite a workout! But let's do the math.

First, we need to find the total distance traveled by the tine in one cycle (or one complete oscillation). The distance traveled in one cycle is simply twice the amplitude, which is 0.13 cm * 2 = 0.26 cm.

Since the tuning fork oscillates at a frequency of 200 Hz, it completes 200 cycles in one second. So, in one second, the distance traveled by the tine is 0.26 cm * 200 cycles = 52 cm.

Now, we need to calculate the total distance traveled by the tine in 1.0 minute, which is 60 seconds. Therefore, the total distance traveled by the tine in 1.0 minute would be 52 cm * 60 seconds = 3120 cm.

So, the tine of the tuning fork travels a total distance of 3120 cm in 1.0 minute. That's quite an impressive journey for a little tine!

To find the total distance traveled by the tine in 1.0 minute, we need to calculate the distance traveled in one vibration and then multiply it by the number of vibrations that occur in 1.0 minute.

First, let's find the distance traveled in one vibration. The amplitude of the tuning fork gives us the maximum displacement from its equilibrium position. So, the distance traveled in one vibration is twice the amplitude.

Distance traveled in one vibration = 2 × amplitude
Distance traveled in one vibration = 2 × 0.13 cm
Distance traveled in one vibration = 0.26 cm

Next, we need to calculate the number of vibrations that occur in 1.0 minute. Since the frequency of the fork is given in Hz (cycles per second), we can use the following formula:

Number of vibrations = frequency × time
Number of vibrations = 200 cycles/second × 60 seconds
Number of vibrations = 12000 cycles

Finally, we can find the total distance traveled by multiplying the distance traveled in one vibration by the number of vibrations:

Total distance traveled in 1.0 minute = distance traveled in one vibration × number of vibrations
Total distance traveled in 1.0 minute = 0.26 cm × 12000 cycles
Total distance traveled in 1.0 minute = 3120 cm

Therefore, the total distance traveled by the tine of the tuning fork in 1.0 minute is 3120 cm.