#6 #10 #14 #18 #246. If a very long pendulum has a frequency of 0.2 Hz, how long does it take the pendulum to complete one cycle?
The period, which is the time for the pendulum to complete one cycle, is the inverse of the frequency. Therefore,
10. A girl with a mass of 40 kg is swinging from a rope with a length of 2.5 m. What is the frequency of her swinging?
Since the frequency is the reciprocal of the period, we first determine the period of the simple pendulum and then take the reciprocal of that period to determine the frequency.
14. The highly idealized wave pulses shown in the figure below, at a time we shall call zero, have the same amplitudes and travel at 1 cm/s as shown. Draw the shape of the rope at 2, 4, 5, and 8 s.
At two seconds, the bottom wave has moved to the right 2 cm, while the wave on the top has moved to the left 2 cm. At this time the waves do not overlap.
How to get the two-second string configuration.At four seconds the bottom wave has moved to the right 4 cm from its initial position, while the top wave has moved 4 cm to the left from its initial position. Since the individual waves overlap, we are careful to add the contributions.
How to get the four-second string configuration.At the time of five seconds the bottom wave is 5 cm to the right of its original position and the top wave is 5 cm to the left of its initial position.
How to get the five-second string configuration.Finally, at eight seconds the bottom wave is 8 cm to the right of its initial position, while the top wave is 8 cm to the left of its original posiition. As at two seconds, the waves no longer overlap.
How to get the eight-second string configuration.18. Sound waves in iron have a speed of about 5100 m/s. If the waves have a frequency of 300 Hz, what is their wavelength?
The speed of a wave is its frequency times its wavelength. Denoting the speed of sound with a lower case "c," we solve for the wavelength and insert the given values to find the wavelength.
24. The speed of sound waves in aluminum is 5100 m/s. What is the fundamental frequency for standing waves in a 2 meter aluminum rod if it is held at its center?
Denoting the speed of sound with c, we begin by writing the speed of sound is the wavelength times the frequency. Since we are asked to find a frequency we solve for the frequency of the wave.
The wavelength is determined by considering the constraints. Since the rod is held in the center, it cannot move at that position. Thus, there is a node at the rod's center. The ends of the rod are free, so there are antinodes located at the ends of the rod. Therefore, one-half of a wavelength fits along the rod of length L. With this, we can compute the wavelength.
With the speed and wavelength in hand, we solve for the fundamental frequency.
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