Help with questions 1, 3, 4, 5, 7, 8. Thank you.

A wire vibrates with a single loop at 8 Hz. The length of the wire is 4m. The mass of the wire is 40 grams. a. What is the speed of the traveling waves along the wire? b. What is the tension in the wire? c. If the wave travels at the same velocity, calculate its frequency when it is in its 5th mode of vibration. d. Draw a sketch of the mode of vibration above, labeling the nodes and antinodes. e. What effect would the following have on the fundamental frequency? i. Increasing the tension of the wire. ii. Increasing the mass of the wire. iii. Increasing the length of the wire. 2. Two cars are traveling on the highway in opposite directions. The first car is traveling 26.4 m/s east, and the second car is traveling 23.9 m/s west. The first car honks its horn, which has a frequency of 405 Hz. WOH a. What frequency does a person in the second car hear as the first car approaches? b. What frequency does a person in the second car hear as the first car departs? The simple pendulum shown in Case A consists of a mass M attached to a massless string of length L. If the mass is pulled to one side a small distance and released, it will swing back and forth. Cases B, C, and D are variations of this system. A B C D 2.M M M 2M a. Rank the oscillation frequencies of the masses from greatest to least. b. Rank the period of oscillation for the masses from greatest to least. A vibrating string has a frequency of 200 Hz. What will its frequency be if: a. Its length is decreased to 1/4 of its original length? b. Its tension is quadrupled?A string of 80.0 cm long has a fundamental frequency of 300 Hz. If the length of the string is changed to 40.0 cm without changing the tension, what will the fundamental frequency become? 6. A police car with a 600 Hz siren is traveling along the same street as a motorcycle. The velocities of the two vehicles and the distance between them are given in each figure below. Case A Case B 10 m/s 10 m/s 20 m/'s 10 m/s 40 m 25 m Case C Case D 20 m/s 10 m/'s 20 m/s 20 m/s - 25 m 40 m Rank the frequency of the siren as measured by the motorcycle rider from greatest to least. 7. A string 1.0 m long produces a sound of 480 Hz. How many vibrations per second will be produced if the string is: a. 33.3 cm long b. 25 cm long c. 50 cm long d. 10 cm long You see a lightning strike and you hear it approximately 3 seconds later. How far are you from where the lightning strike occurred? 9. A mass m at the end of a spring vibrates with a frequency of 0.88Hz. When an additional 600g mass is added to m, the frequency is 0.60Hz. What is the value of m? 10. A pipe that is closed at one end can be made to resonate by a tuning at a length of 0.25 m. The next resonant length is 0.75 m. If the speed of sound is 338 m/s, calculate: a. The wavelength of the sound emitted by the tuning fork. b. The frequency of the tuning fork 11. A closed air column is 60.0 cm long. Calculate the frequency of forks that will cause resonance at: (speed of sound is 344 m/s) a. First resonant length b. Second resonant length c. Third resonant length