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PHY 111 Lesson 12 Problem Set 6 Name ___________________________ Waves Section ___________ 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. x = 5.0 m t = 10 s 2. t = 50 sec r = 0.26 m 3. f = 240 Hz 4. N/A 5. b) x = 2.0 m 6. N/A 1. A student holding one end of a rope moves her hand up and down twenty times in t seconds generating waves on the rope. Another student measures that the distance from one crest to another is x meters. a) What is the wavelength? (3 pts) Wavelength formula: lambda = wave velocity/frequency Frequency of wave: 20/t Wavelength = wave velocity (x) /20/t OR (x * 20)/t Wavelength = 5.0m *20 /10s = 10m

b) What is the wave frequency? (3 pts) The frequency is the number of waves per second, so that number, divided by t, or time. The student moved her hand 20 times, and the time given is 10s, so the frequency of the wave is 20/10Hz, or 2Hz. c) What is the wave period? (3 pts) Since 2 waves are generated per second (as shown in part B), we take the inverse of this to find the period, or formula T = 1/f. T= 1/2Hz or 0.5 seconds is the period of the wave. d) What is the speed of the traveling waves? (3 pts) We take the frequency (2Hz), and the wavelength (10m) and multiply them together with the formula v=λf, to find the speed of the waves. V= 10*2 or 20 m/s. e) 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? Be specific. (2 pt each) i) Wavelength As the frequency decreases, the wavelength increases and doubles. It takes double the time for a wave to be created. ii) Period If the frequency halves, the period doubles, as they are exact inverses. iii) Wave speed The wave speed is independent of the wave frequency, so the wave speed will not change. 2. 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)

To find the intensity of the wave, we can use the formula I = P/A, where P is the Power (work done each second – in joules for this instance), and A is the area. P is 2000J/50 seconds, or 400 J/sec, and the Area is 0.26m, which must be squared to find the A (0.0676m). I = 400/0.0676 or 5917.16 OR 5. 92 * 10 5 W/m 2 3. 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) The formula for the Doppler effect is: f = f 0 * (v + v r ) / (v + v s ) - f is the frequency of the sound heard by the student. - f 0 is the frequency of the sound produced by the car engine. - v is the speed of sound in air. - v r is the velocity of the student relative to the air. - v s is the velocity of the car relative to the air. If the student hears a frequency of 240 Hz, we can use the formula above to calculate the velocity of the car relative to the air: 240 = 250 * (v/v-v s ) Simplifying this equation, we get: 240 = 250 * (343/343-v s ) The value of the speed of sound in air is v = 343 m/s, and the frequency of the sound produced by the car engine is f 0 = 250 Hz, we get: v s = (250 * 343/343)/240 or The motion of the car is 13.02 m/s towards the student. 4. Sketch a transverse representation of a sound wave that is both loud and high pitch. Briefly explain your diagram. (3 pts)

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Higher pitched sounds have a higher frequency and shorter wavelength, in addition to a larger amplitude (louder sound), which is shown here. 5. A student blows across the top of an empty bottle creating a standing wave of air particles inside the bottle. The standing wave inside the bottle is a quarter of a wave (see below). The student adds water to the bottle and blows across the top producing a new standing wave inside the bottle (see below). Compare the pitch of the new sound wave to the pitch of the original sound wave and explain your reasoning. (4 pts) The length of the bottle determines the pitch of the soundwave since it affects the amplitude of the wave (softer and louder sound determinants). If the amplitude is shorter, it produces a softer sound, and we don’t know how the wavelength changed really because from my point of view it looks the same in both pictures. b) The bottle has a length of x meters. The speed of a sound wave is 340 m/s. What is the frequency of the original sound wave? (hint: recall that there is only a quarter of a sound wave inside the original bottle) (4 pts) We can use the formula frequency = wave velocity/wavelength to find the frequency of the original sound wave. The wavelength can be given by dividing the given length of the bottle by 4, getting 0.5m as the wavelength. If we substitute the speed of the sound wave into the equation, we get 340m/s / 0.5m or a frequency of 680 Hz.

6. 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 each) a) b)

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