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ffPHYSICS DEPARTMENT - KFUPM
Review : Chapter 17-18 Sup. & Standing Waves
Q 1. The wave function for a standing wave in a string is given by
y = 0.12 sin (PI * x) cos (4 * PI * t)
where x and y are in m and t in s. Find the three smallest values of x corresponding to maximum displacement of the motion (anti nodes).
(Ans: 50 cm, 150 cm, 250 cm).
Q 2. Two sinusoidal waves, having equal frequency and amplitude and traveling with the same speed in the same direction, are combined. Determine the amplitude of the resulting motion if the amplitude of each wave is 5.00 cm and the two waves differ in phase by (PI/3) radians. (Ans. 8.7 cm)
Q 3. Two speakers S1 and S2 are driven by the same oscillator at a frequency of 390 Hz. A listener is originally located at P ( Fig. 1)
Q
S1
O P
S2
Fig.1
The listener walks in a direction perpendicular to OP until he reaches point Q where the intensity of sound is minimum. If the difference between QS2 and QS1 is 44.5 cm, what is the speed of sound in the air at the time of the experiment ? (Ans: 347 m/s)
Q 4. We want to measure how deep a water well is from the resonance condition of the well. A big speaker driven by a frequency generator is placed near the mouth of the well. Two consecutive resonances are observed, one at 155 Hz and the other at 165 Hz. Assuming the velocity of sound is 340 m/s, find how deep the well is. (Ans: 17 m)
Q 5. A tube, initially open at both ends, is observed to resonate at a frequency of 1000 Hz ( not necessarily the fundamental frequency). When one end of the tube is closed a resonant frequency of 250 Hz is observed (again, not necessarily the fundamental frequency). What is the minimum pipe length satisfying these conditions ? Take the speed of sound in air to be 343 m/s. (Ans.34.3 cm)
Q 6. The minimum length of a pipe, closed at one end that resonates with a given source of sound is 7.0 cm. Taking the speed of sound in air as 350 m/s, calculate the frequency of the source of sound. (Ans. 1250 Hz)
Q 7. When a sound generator sweeps through all frequencies between 1000 Hz and 2000 Hz, resonance is excited in a hollow tube at just two frequencies, at 1400 Hz and 1800 Hz. The tube is open to the air at one end and closed at the other. Find the fundamental resonance frequency for the tube. (Ans. 200 Hz)
PHYSICS DEPARTMENT - KFUPM
Review : Chapter 18 sound Waves
Q 1. In the sonar method of measuring distances under water, a sound pulse travels from
The generator to a distant object and is reflected back to the location of the generator.
If the bulk modulus of sea water is 2.16 x 109 N/m2 and the density of sea water is
1.022x103 Kg/m3, what is the time interval between sending out and receiving the
reflected pulse from an object 1200m away ? (Ans. 1.65 s).
Q 2. A steel rail on a railroad is struck with a hammer by a worker. A listener some
distance d from the worker with one ear on the rail hears two sounds separated in time
by 2.0 s. One sound wave corresponds to waves travelling through the air, the other
through the rail. Find the distance d, assuming the rail is straight. (For steel young
modulus = 20 x 1010 N/m2 and density = 7.86x103 kg/m3. Speed of sound in air = 343
m/s). (Ans: 736 m)
Q 3. By what factor must the pressure amplitude of a harmonic sound wave be increased in order to increase the intensity by a factor of 16 ? (Ans: 4)
Q 4. A sound wave travels in a medium of density 1.2 kg/m**3. The displacement, s, of the molecules of the medium from their equilibrium position is given by:
S = 0.00060 cos (PI(( 5.83 x) (2000 t ))) m, where x is in m and t is in s. What is the pressure amplitude of the wave ? (Ans: 1.55x104)N/m2)
Q 5. A sound wave with an intensity level of 65.0 dB strikes an eardrum of area 7.85x10-5m2. How much energy is absorbed by the eardrum per second ? Assume that all energy is absorbed by the eardrum (Ans: 2.48x10-10J)
Q 6. The sound level of a jet airplane is measured as 150 dB and that of a vacuum cleaner as 70 dB. If the intensity from the jet is I1 and the intensity of the sound from the vacuum cleaner is I2, what is the ration I1/I2 ? (Ans: 108)
Q 7. Two cars are traveling, one behind the other, in the same direction along the same straight road. The car in front has a speed of 20 m/s and the car behind has a speed of 23 m/s. The horn of the car behind is sounded at a frequency of 1280 Hz. What is the apparent frequency of the horn as observed by an occupant of the leading car ? take the speed of sound as 343 m/s. (Ans: 1292 Hz).
Q 8. An approaching rain sounds its whistle and appears to have a frequency of 280 Hz, according to passengers waiting at the station. The frequency experienced by the passengers aboard the train is 262 Hz. The velocity of the sound in air is 1080 ft/s under prevailing condition. Find the speed of the train. (Ans: 69.4 ft/s)
PHYSICS DEPARTMENT - KFUPM
Review : Chapter 19 Temp & Thermal Expansion
Q 1. At what temperature do the Fahrenheit and Celsius scales coincide ?
(Ans: 40o C)
Q 2. A substance is heated from 90o F to 315o F. What is the change in temperature on (i) the Celsius and (ii) the Kelvin scales ?
( Ans: (i) 125o C (ii) 125 Ko)
Q 3. A new temperature scale called Mew, is invented whereby on this cale the ice point is 40o Mew and the steam-point is 190o Mew. What is the Celsius reading when the temperature on the Mew scale is 20o Mew ? (Ans: 40oC)
Q 4. A steel rod is 3.000 cm in diameter at 25 oC. A brass ring has an inner diameter of 2.992cm at 25o C. At what common temperature will the ring just slide onto the rod ? ( Alpha (steel) = 1.00 x 10-5/oC, Alpha (brass) = 2.00 x 10-5/oC ) (Ans: 293oC)
Q 5. A metal cube 0.1m on a side is heated from 10oC to 30oC. What is the decrease in its density ? ( Alpha (metal) = 3.4 x 10-5 /oC, Density of the metal at 10o C = 2.7 x 103 Kg/m3) (Ans: 3.88 Kg/m3)
Q 6. A copper rod has a diameter of 5.000 cm and a length of 25.000 cm at 20o C. At 100 oC the length of the rod is 25.034 cm. What is the fractional change in volume of the rod when the temperature of the rod increases form 20oC to 100oC ?
(Ans: 4.08x103)
Q 7. A helium storage tank has a capacity of 0.05 m3. If the gas pressure is 100 atm at 27oC, determine the mass of He in the tank. The molecular mass of helium is 4 grams/mole. (Ans:812g)
Q 8. How many molecules are there in 1 liter of an ideal gas at 0oC and 1 atm ?
(Ans: 2.7x102)
Q 9. A cylinder contains helium at 20oC and pressure of 15 atm at a volume of 12 liters. The temperature is raised to 35 oC and the volume reduced to 8.5 liters. What is the final pressure of the gas. Assume the gas is ideal. (Ans: 22 atm)
Q 10. As a result of a temperature rise of 32oC, a bar with a crack at its center buckles upward as shown in the figure. If the fixed distance Lo = 3.77m and the coefficient of linear expansion is 25x10-6 oC, find x, the distance to which the center rises.
( Ans: 7.5 cm)
PHYSICS DEPARTMENT - KFUPM
Review : Chapter 19-20 Heat & First Law of Thermodynamics
Q 1. A block of copper of mass 500 g is dropped into a copper calorimeter of mass 200 g which contains 250 g of water at 25oC. This causes the water to boil and 8.0 g are changed into steam. The heat of vaporization of water is 540 cal/g and the specific heat of copper is 0.0923 cal/ g oC). What was the temperature of the copper block ? (Neglect neat losses to the environment). (Ans: 630oC)
Q 2. A 50 kg block of ice at 0oC is given an initial speed of 5.4 m/s along a rough horizontal surface. The block slides a distance of 28.3 m before coming to rest. How much ice melts during this time ? Take heat of fusion of water to be 3.3x105 J/Kg. (Ans: 2.2 g)
Q 3. A rod made of copper has a length of 1 m. The cross-sectional area of the rod is 1 cm2. one end is maintained at the steam point (100 oC) and the other end kept at 0 oC with a large block of ice. How much ice melts in one hour ? Take latent heat of fusion of water to be 80 cal/g and the themal conductivity of copper to be 0.95 cal/(s.cm.C deg). (Ans: 43 g)
Q 4. How much ice at - 20 deg C must be dropped into 0.25 kg of water initially at 20oC in order for the final temperature to be 0oC with all the ice melted ? The heat capacity of the container may be neglected. Specific heat of ice = 0.48 cal/g oC; heat of fusion of water = 80 cal/g. (Ans: 55.8 g)
Q 5. Five moles of an ideal gas undergoes an isothermal compression at 100oC in which the final volume is one half the initial volume. What is the work done on the gas for this process ? (Ans: 10.75x103 J)
Q 6. An Ideal gas initially at 0oC and 1 atm pressure is compressed isothermally from an initial volume of 6x104 cm 3 to a final volume of 2x104 cm3. What is the heat flow from the gas during the process ? (1 atm pressure = 1.01x105 N/m2). (Ans. 1590 cal)
Q 7. An Ideal gas is carried around the cycle shown in Fig.1. Calculate the amount of heat supplied to the gas in each cycle. (Ans. 213 cal)
Q 8. An ideal gas goes from A to B in the process shown in Fig. 2. In this process the internal energy of the gas increases by 500 cal. How much heat is supplied to the gas in this process ? (Ans. 5130 J)
Q 9. A gas is compressed at constant pressure of 0.2 atm from a volume of 10 liters to a volume of 4 liters. In this process, 500 J of heat flow out of the gas. What is the change in the internal of the gas ? (Ans: 380 J)
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