Lesson 12 Problem Set 6 Completed

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Apr 3, 2024

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PHY 111 Lesson 12 Problem Set 6 Name Sydney Hveem Waves Section 12670 Directions: Several of the following problems are missing some of the given variable information. Your instructor will provide the values through email in the “From Your Instructor” section of the weekly lesson or in a course announcement. Use the values provided by your instructor to answer all of the questions. Show all your work . Make sure to use appropriate labels and units, and highlight your final answers if they are numerical. 1. Two students stand x meters apart with a rope stretched between them. One student moves her hand up and down 25 times in t seconds, which causes a standing wave with n total nodes to form. Nodes = 4 Space = 2 m Time = 5 s a) Sketch a picture of the standing wave that forms. (2 pts) b) What is the wavelength? (3 pts) 4 nodes = 2.0 meters Wavelength = 0.25 m

c) What is the wave frequency? (3 pts) F = # of waves/time F = (25 waves)/(5.0 s) = 5.0 Hz d) What is the wave period? (3 pts) v = λf v = (0.25 m)(5.0 Hz) v = 1.25 m/s e) What is the speed of the traveling waves? (3 pts) T = 1/f T = 1/(5.0 Hz) T = 0.2 s f) The student halves the number of times she moves her hand up and down each second. What effect does this have on each of the following? (1 pt each) i) Wavelength The wavelength will get longer as the frequency decreases. ii) Period The period will increase as the frequency decrease. iii) Wave speed The wave speed will not change as it is independent of the frequency.

g) How many times should the student move her hand up and down to create the first harmonic (i.e., the fundamental frequency)? (3 pts) F = v/2L F = (1.25 m/s)/(2*2m) = 0.31 Hz 2. A student blows across the top of an empty bottle causing it to resonate at its fundamental frequency. The bottle has a height of h. The speed of sound is 340 m/s. What is the fundamental frequency? (4 pts) Height = 0.220 m (0.220m)/(1/4 wave) = 0.88 m F = (340 m/s)/(2*0.88m) = 193.2 Hz b) What is the bottle’s third harmonic (i.e., second overtone)? (3 pts) (0.220m)/(5/4 wave) = 0.18 m 3 rd Harmonic = (340 m/s)/(2*0.18m) = 944.4 Hz 3. A wave delivers 2000 J of energy every t seconds to a circular area with radius r. What is the intensity of the wave? (4 pts) Radius = 0.25 m Time = 2 s I = P/A I = (2000 J)/(2 s)/( π(0.25m) 2 ) = 5102.04 W/m 2

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4. A particular car engine produces a frequency of 250 Hz. A student listening to the engine of the car hears a frequency of f. Describe the motion of the car relative to the student. (3 pts) Frequency = 260 Hz 260 Hz = 250 Hz((343 m/s)/(343 m/s – v s ) 260 Hz(343 m/s – v s ) = 250 Hz * 343 m/s V s = (343 m/s(260 Hz – 250 Hz))/(260 Hz) = 13.19 m/s 5. Two students produce a wave pulse on either end of a rope as shown below. Sketch the waveform that results from the superposition of the two pulses (i.e., show what happens when the two wave pulses collide). (2 pts) a) b)

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