2. A pendulum oscillates 21 times in 30 seconds. a. What is the frequency of the pendulum’s oscillations ?b. What is the period of the pendulum’s oscillations ? c. What is the length of the pendulum?( Round answer to the nearest centimeter)
Simple harmonic motion
Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.
Simple Pendulum
A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.
Oscillation
In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.
1. a) Using the diagram below, determine the wavelength and amplitude of the sound wave below. b) If the wave speed was given as v = 340 m/s, what is the frequency (Hz) of this wave? c) Is the frequency in the audible range?
2. A pendulum oscillates 21 times in 30 seconds. a. What is the frequency of the pendulum’s oscillations ?b. What is the period of the pendulum’s oscillations ? c. What is the length of the pendulum?( Round answer to the nearest centimeter)
3. A pendulum is 0.65 meters long. a) What is the period of oscillation? b) What is the frequency of its oscillations? Round to the nearest hundredth.
4. A water wave has a frequency of 2 Hz, and there are 5 meters between each crest on the wave. a) How fast is the wave moving? b) What is the period of the wave?
5. Sound waves travel at roughly 340 m/s at room temperature. The minimum hearing range of a human is 20Hz. a) What is the wavelength of this wave? b) Could this wavelength fit inside the dimensions of Room 411( room dimensions are roughly 11.5 m x 8.7 m)? Justify your answer with sound reasoning (pun intended :-))
6. If a spring requires 20 N to be compressed a distance of 10 centimeters, a) What is the spring constant in N/m? b) How much force is required to compress the spring 15 cm? c) How much PE (J) is stored in the spring when it is compressed to 15 cm?
7. Jenny and her friend Elaine are attending a rock concert. Elaine had special tickets to the VIP area and is standing 10 m from the stage. Using her portable equipment, she determines that the noise in her section is 100 decibels. Jenny had cheaper tickets and is standing 100 m away. a) Using the inverse square law, how does the sound intensity compare where Jenny is (100 m from the stage) compared to where Elaine is (10 m from the stage)? b) How loud is it where Jenny is standing (in dB)?
8. a) Determine the wavelength of the longitudinal wave below. b) Given a wave speed of 340 m/s, determine the frequency of this wave? (Round your answer to the nearest tenth) c) What is the period of the wave? (Round your answer to the nearest millisecond).
9. The speed of sound is temperature dependent and can be determined by the formula: v(sound) = 331 + 0.6 T(C), where v is the speed of sound in m/s and T is temperature in degrees C. If a sound wave is determined to have a frequency of 1,000 Hz and a wavelength of 35 cm. a) What is the speed of this wave? b) Use the given formula to determine the temperature of the air? c) Based on your temperature result, how would you categorize the air as WARM or COLD?
10. The hottest recorded temperature in the history of the United States is 134 °F, which is 57 °C. What is the speed of sound at this temperature?
11. a) How does the speed of sound in air compare to the speed of sound in water? How does the speed of sound in air compare to the speed of sound in steel?
12. On May 26, 2022 one of the strongest earthquakes for the year was a magnitude 7.2 in Southern Peru on the Richter scale. a) Based on the image describe the FOCUS and EPICENTER of the earthquake. b) Determine the amount of energy released in ergs, and c) Determine the amount of energy released in Joules.
13. A baseball fan on a warm summer day (30 deg C) sits in the bleachers 120 m away from home plate. a) What is the speed of sound in air at 30 deg C? b) How long after seeing the ball hit the bat does the fan hear the crack of the bat? (Round answer to nearest hundredth).
15. An oceanic depth-sounding vessel surveys the ocean bottom with ultrasonic sound that travels 1530 m/s in seawater. Find the depth of the water if the time delay of the echo to the ocean floor and back is 8 seconds
16. Determine the gravitational force of attraction between the Earth and Jupiter given the mass of the earth is 6 x 10^24 kg, the mass of Jupiter is 1898.6 x 10^24 kg and the closest distance is about 5.88 x 10^11 m. Use scientific notation for final result. Use G= 6.7 x 10^-11 N-m^2/kg^2.
17. Home smoke detectors often contain the radioactive element Americium-241 which emits α particles with energies of about 5.4 MeV, which are stopped by a piece of paper or a few centimeters of air and cannot penetrate the human epidermis. a) Write the alpha decay formula that shows what Am-241 decays into. b) How many protons does Am
18. a) How much louder is a 90 dB sound compared to a 50 dB sound? b) Based on the chart describe the sound level (give example) at 50 dB and c) at 90 dB-241 have and how do you know? c) How many neutrons does Am-241 have and how do you know? d) How many electrons does an electrically neutral atom of Am-241 have?
19. A submarine is moving toward another submarine at 9.2 m/s. it emits a 3.5 MHz ultrasound. What frequency would the second sub, at rest, detect? The speed of sound in water is 1482 m/s.
20. If you shout across a canyon and hear the echo 0.80 s later, how wide is the canyon?
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