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PHYS-2325: University Physics-I Khalid Bukhari Ch-15 NAME: _____________________________________________ HOMEWORK CHAPTERS 15 TO 18 NOTE: 1 Hand in your solutions in class in the lecture period after which the chapter is completed. 2 Show the equations and calculations, and box your answer. Be sure to include the units. 3 You are required to solve all problems. Instructor will select and grade any four questions, and the marks for this HW will be based on these only. Chapters 15 : OSCILLATORY MOTION 1. In an engine, a piston oscillates with simple harmonic motion so that its position varies according to the expression below, where x is in centimeters and t is in seconds. Find the period of the motion. x 5.00 cm cos 2t 6 2. A simple harmonic oscillator takes 12.0 s to undergo five complete vibrations. Find the angular frequency in radians per second. 3. A piston in a gasoline engine is in simple harmonic motion. Taking the extremes of its position relative to its center point as ±5.00 cm, find the maximum velocity of the piston when the engine is running at the rate of 3600 rev/min. 4. A simple pendulum has a mass of 0.250 kg hanging by a string of length of 1.00 m. It is displaced through an angle of 15.0° and then released. Where will the tension in the string be maximum. 1 PHYS-2325: University Physics-I Khalid Bukhari Ch-15 5. A 0.500-kg object attached to a spring with a force constant of 8.00 N/m vibrates in simple harmonic motion with an amplitude of 10.0 cm. Calculate (a) the maximum value of its speed and acceleration, (b) the speed and acceleration when the object is 6.00 cm from the equilibrium position, and (c) the time interval required for the object to move from x = 0 to x = 8.00 cm. (no Q 6, 7) 8 - 11 A 2.00-kg object is attached to a spring and placed on a horizontal, smooth surface. A horizontal force of 20.0 N is required to hold the object at rest when it is pulled 0.200 m from its equilibrium position (the origin of the x axis). The object is now released from rest with an initial position of xi = 0.200 m, and it subsequently undergoes simple harmonic oscillations. Find (8) the force constant of the spring, (9) the frequency of the oscillations, and (10) the maximum speed of the object. Where does this maximum speed occur? (11) Find the maximum acceleration of the object. 2 PHYS-2325: University Physics-I Khalid Bukhari Ch-15 12. While riding behind a car traveling at 3.00 m/s, you notice that one of the car’s tires has a small hemispherical bump on its rim as shown in Figure P15.23. If the radii of the car’s tires are 0.300 m, what is the bump’s period of oscillation? 13. A simple pendulum is 5.00 m long. What is the period of small oscillations for this pendulum if it is located in an elevator accelerating upward at 5.00 m/s 2? Chapter 16: WAVE MOTION 1 A sinusoidal wave is traveling along a rope. The oscillator that generates the wave completes 40.0 vibrations in 30.0 s. Also, a given maximum travels 425 cm along the rope in 10.0 s. What is the wavelength of the wave? 3 PHYS-2325: University Physics-I Khalid Bukhari Ch-15 2. For a certain transverse wave, the distance between two successive crests is 1.20 m, and eight crests pass a given point along the direction of travel every 12.0 s. Calculate the wave speed. 3. A wave is described by y = (2.00 cm) sin (kx t), where k = 2.11 rad/m, = 3.62 rad/s, x is in meters, and t is in seconds. Determine the amplitude, wavelength, frequency, and speed of the wave. 4. A seismographic station receives S and P waves from an earthquake, 17.3 s apart. Assume the waves have traveled over the same path at speeds of 4.50 km/s and 7.80 km/s. Find the distance from the seismograph to the hypocenter of the earthquake. 5. A piano string having a mass per unit length equal to 5.00 10–3 kg/m is under a tension of 1 350 N. Find the speed with which a wave travels on this string. 4 PHYS-2325: University Physics-I Khalid Bukhari Ch-15 6. Transverse pulses travel with a speed of 200 m/s along a taut copper wire whose diameter is 1.50 mm. What is the tension in the wire? (The density of copper is 8.92 g/cm 3.) 7 An astronaut on the Moon wishes to measure the local value of the free-fall acceleration by timing pulses traveling down a wire that has an object of large mass suspended from it. Assume a wire has a mass of 4.00 g and a length of 1.60 m and assume a 3.00-kg object is suspended from it. A pulse requires 36.1 ms to traverse the length of the wire. Calculate gMoon from these data. (You may ignore the mass of the wire when calculating the tension in it.) Chapter 17: SOUND WAVES 1 Suppose you hear a clap of thunder 16.2 s after seeing the associated lightning stroke. The speed of sound in air is 343 m/s, and the speed of light in air is 3.00 108 m/s. How far are you from the lightning stroke? Do you need to know the value of the speed of light to answer? Explain. 2. A dolphin in seawater at a temperature of 25°C makes a chirp. How much time passes before it hears an echo from the bottom of the ocean, 150 m below? 5 PHYS-2325: University Physics-I Khalid Bukhari Ch-15 3. The area of a typical eardrum is about 5.00 10–5 m2. Calculate the sound power incident on an eardrum at (a) the threshold of hearing and (b) the threshold of pain. 4 A driver travels northbound on a highway at a speed of 25.0 m/s. A police car, traveling southbound at a speed of 40.0 m/s, approaches with its siren producing sound at a frequency of 2 500 Hz. (A) What frequency does the driver observe as the police car approaches? And after the police car passes him? (B) Repeat part (A) for the case when the police car is also traveling north. 5. Standing at a crosswalk, you hear a frequency of 560 Hz from the siren of an approaching ambulance. After the ambulance passes, the observed frequency of the siren is 480 Hz. Determine the ambulance’s speed from these observations. 6 PHYS-2325: University Physics-I Khalid Bukhari Ch-15 6. A flowerpot is knocked off a balcony 20.0 m above the sidewalk and falls toward an unsuspecting 1.75-m-tall man who is standing below. How close to the sidewalk can the flowerpot fall before it is too late for a warning shouted from the balcony to reach the man in time? Assume the man below requires 0.300 s to respond to the warning. The ambient temperature is 20°C. 7 W/m2. Calculate the sound level (in decibels) of a sound wave that has an intensity of 4.00 8 A fireworks rocket explodes at a height of 100 m above the ground. An observer on the ground directly under the explosion experiences an average sound intensity of 7.00 10–2 W/m2 for 0.200 s. (A) What is the total sound energy of the explosion? (B) What is the sound level (in decibels) heard by the observer? 7 PHYS-2325: University Physics-I Khalid Bukhari Ch-15 Chapter 18: SUPERPOSITION AND STANDING WAVES 1. Two waves in one long string are described by the wave functions: y1 = 3.0 Cos(4.0x – 1.6t) and y2 = 4.0 Sin(5.0x – 2.0t) where x and y are in cm and t is in seconds. Find the value of y when the two waves are in superposition at a point x=1.0 cm and t=0.5s. 2. A string is stretched and fixed at both ends, 200 cm apart. If the density of the string is 0.015 g/cm, and its tension is 600 N, what is the wavelength (in cm) of the first harmonic? 3. A stretched string is observed to vibrate in three equal segments when driven by a 480 Hz oscillator. What is the fundamental frequency of vibration for this string? 4. Two tuning forks with frequencies 264 and 262 Hz produce "beats". What is the beat frequency (in Hz)? 8