Name You will need to be able to: Waves and Sound Final Review 1) Describe parts of waves, use wave equation, and determine frequency and period. 2) Distinguish between transverse and longitudinal waves, and apply the principle of superposition. 3) Describe sound waves and solve problems involving Doppler effect. 4) Solve problems about and describe resonance in closed tubes, open tubes and strings. Review Notes:
1) A wave is introduced into a thin wire held tight at each end. It has an amplitude of 3.8 cm, a frequency of 51.2 Hz and a distance from a crest to the neighboring trough of 12.8 cm. Determine the period of such a wave. 2) A fly flaps its wings back and forth 121 times each second. The period of the wing flapping is seconds. 3) A tennis coach paces back and forth along the sideline 10 times in 2 minutes. The frequency of her pacing is Hz. 4) Non-digital clocks (which are becoming more rare) have a second hand that rotates around in a regular and repeating fashion. The frequency of rotation of a second hand on a clock is Hz. 5) Olive accompanies her father to the park for an afternoon of fun. While there, she hops on the swing and begins a motion characterized by a complete back-and-forth cycle every 2 seconds. a. What is the frequency of the swing? b. What is the period of the swing?
6) A period of 5.0 seconds corresponds to a frequency of 7) A common physics lab involves the study of the oscillations of a pendulum. If a pendulum makes 33 complete back-and-forth cycles of vibration in 11 seconds, what is its frequency and period? 8) The water waves to the right are traveling along the surface of the ocean at a speed of 2.5 m/s and splashing periodically against Wilbert's perch. Each adjacent crest is 5 meters apart. The crests splash Wilbert's feet upon reaching his perch. How much time passes between each successive drenching? 9) A ruby-throated hummingbird beats its wings at a rate of about 70 wing beats per second. a. What is the frequency in Hertz of the sound wave? b. Assuming the sound wave moves with a velocity of 340 m/s, what is the wavelength of the wave?
10) Ariel cuts short sections of PVC pipe into different lengths and mounts them in putty on the table. The PVC pipes form closed-end air columns that sound out at different frequencies when she blows over the top of them. The actual frequency of vibration is inversely proportional to the wavelength of the sound; and thus, the frequency of vibration is inversely proportional to the length of air inside the tubes. Express your understanding of this resonance phenomenon by filling in the following table. A B C D E F 11) A guitar string with a length of 80.0 cm is plucked. The speed of a wave in the string is 400 m/s. Calculate the frequency of the first, second, and third harmonics.
12) A pitch of Middle D (first harmonic = 294 Hz) is sounded out by a vibrating guitar string. The length of the string is 70.0 cm. Calculate the speed of the standing wave in the guitar string. 13) A frequency of the first harmonic is 587 Hz (pitch of D5) is sounded out by a vibrating guitar string. The speed of the wave is 600 m/s. Find the length of the string. 14) Stan is playing his open-end pipe. The frequency of the second harmonic is 880 Hz (a pitch of A5). The speed of sound through the pipe is 350 m/s. Find the frequency of the first harmonic and the length of the pipe. 15) On a cold day, Michael blows on a toy flute, causing resonating waves in an open-end air column. The speed of sound through the air column is 336 m/s. The length of the air column is 30.0 cm. Calculate the frequency of the first, second, and third harmonics.
16) Tommy and the Test Tubes are playing at a night club this weekend. The lead instrumentalist uses a test tube (closed-end air column) with a 17.2 cm air column. The speed of sound in the test tube is 340 m/s. Find the frequency of the first harmonic played by this instrument. 17) Pete is playing at City Park next weekend. One of the closed-end pipes is capable of sounding out a first harmonic of 349.2 Hz. The speed of sound in the pipe is 340 m/s. Find the length of the air column inside the pipe. 18) A science fiction film depicts inhabitants of one spaceship (in outer space) hearing the sound of a nearby spaceship as it zooms past at high speeds. Critique the physics of this film. 19) A transverse wave is observed to be moving along a lengthy rope. Adjacent crests are positioned 2.4 m apart. Exactly six crests are observed to move past a given point along the medium in 9.1 seconds. Determine the wavelength, frequency and speed of these waves.
20) Humpback whales are known to produce a collection of elaborate and repeating sounds with frequencies ranging from 20 Hz to 10 khz. The sound waves travel through water at speeds of approximately 1400 m/s. Determine the wavelengths of the waves at the lower and the upper end of this frequency range. 21) A wave is traveling in a rope. The diagram below represents a snapshot of the rope at a particular instant in time. Determine the number of wavelengths which is equal to the horizontal distance between points a. C and E on the rope. b. C and K on the rope. c. A and J on the rope. d. B and F on the rope. e. D and H on the rope. f. E and I on the rope.
22) A wave with a frequency of 12.3 Hz is traveling from left to right across a rope as shown in the diagram at the right Positions A and B in the diagram are separated by a horizontal distance of 42.8 cm. Positions C and D in the diagram are separated by a vertical distance of 12.4 cm. Determine the amplitude, wavelength, period and speed of this wave. 23) A standing wave pattern is established in a 246-cm long rope. A snapshot of the rope at a given moment in time is shown in the diagram below. Vibrations travel within the rope at speeds of 22.7 m/s. Determine the frequency of vibration of the rope. 24) In a physics lab, a rope is observed to make 240 complete vibrational cycles in 15 seconds. The length of the rope is 2.8 meters and the measurements are made for the 6th harmonic. Determine the speed of the waves in the rope.
25) A 144 cm long rope undergoes exactly 64 complete vibrational cycles in 17.6 seconds when vibrating in the third harmonic. Determine the speed of the waves in the rope. 26) School was letting out at the nearby elementary school when Adam went to pick up his 9 year old kid at the school. He was traveling about 20 m/s when the release bell went off at 350 Hz. What frequency does Adam hear? 27) Sylvia goes speeding by a cop car on the side of the road who is checking speeds. Sylvia was speeding at 23 m/s so the policeman turns on his siren. If the frequency of the siren that the police car emits is 545 Hz, what frequency does Sylvia hear? 28) Given the situation in the last question, although this time the police car is trailing Sylvia at a speed of 10 m/s. What frequency does Sylvia now hear?