1. Assuming the tension in the string is unchanged:

a) What happens to the wavelength of a wave on a string when the frequency is doubled?

b) What happens to the speed of the wave on a string when the frequency is doubled?

2. If the distance from a point source of sound is tripled, by what factor does the sound intensity change? Assume there are no reflections from nearby objects to affect your results.

3. My 25 beagles produce 73 dB's sound intensity level outside my closed door. How many more beagles can I obtain before exceeding the 81 dB limit ?

4. 5 m in front of the stage, The Whichevers produce a 180 dB sound intensity level. How far away would one have to go before they have the same sound intensity level of a mosquito buzzing around (about 40 dB's) ?

5. A train is moving parallel to a highway at 20 m/s. A car is traveling in the same direction as the train at 40 m/s. The car horn sounds at 510 Hz and the train whistle sounds at 320 Hz. When the car is approaching the train from behind, what frequency does an occupant of the car observe for the train whistle?

6. A metal rod made of some alloy is to be used as an thermometer. At 0^o C its length is 40.000 cm, and at 100^o C its length is 40.060 cm. What is its temperature coefficient of linear expansion ?

7. How long does it take to heat 30 g of water from 20 ⁰ C to 80^o C using a 40 watt heater (assuming 85 % efficiency and no heat loss to the surroundings, also, for those of you that do not remember, 1 watt = 1 J/s)) ?

8. Draw a Temperature vs time curve for a :

a. A temperature probe at room temperature placed in 80^o C water.

b. Electronic temperature sensor taken out of water at 20^o C and waved around in a room whose temperature is 25^oC.

9. A piece of aluminum (specific heat .910 joule/gram^oC) of mass 200 grams at 80.0^oC is dropped into a foam cup filled with 100 ml of water at 20^oC. What is the final temperature of the water and aluminum?

10. Imagine you transfer a certain amount of heat to a known amount of a liquid in a perfectly insulated cup and the temperature changes. Then, you decide to alter the experiment in several different ways. For each of the alterations listed below, state whether the change in temperature will be larger, smaller or the same as that measured before the alteration. Briefly explain each answer.

a. Heat for a longer time but transfer the same total heat.

b. Increase the temperature outside of the cup.

c. Start with warmer liquid.

d. Change to an equal mass of liquid with a larger specific heat capacity.

e. Use the same volume of a denser liquid with the same specific heat capacity.

11. Suppose the speed of sound in air depends upon temperature (in degrees Celcius) according to the formula v = 340 + 0.5 T_C and temperature varies with height above sea level according to T_C = T_o + 20 h², where To = the temperature in degrees Celcius at sea level. (I'll sell you a hint for two points cheap!)

a) Find the integral expression that will tell you how long will it take sound from an airplane flying at an altitude 6000 m to reach the ground (sea level) on a day when the ground level temperature is 40^o C ?

b) 10 Pts Bonus! Evaluate this integral. (Note: The answer won't make much sense cuz the problem has been "altered" to make it nice for the kiddies.)