Exam 3: Oscillations, Fluids, Waves, Temperature, Heat, and the First Law of Thermodynamics

Two traveling sinusoidal waves interfere to produce a wave with the mathematical form Y(x,t) = y_m sin(kx + t + $\alpha$ ). If the value of is appropriately chosen, the two waves might be:

Here are the equations for the three waves traveling on separate strings. Rank them according to the maxium transverse speed, least to greatest. Wave 1: y(x,t) = (2.0 mm) sin [(4.0 m^-1)x - (3.0 s^-1)t] Wave 2: y(x,t) = (1.0 mm) sin [(8.0 m^-1)x - (4.0 s^-1)t] Wave 3: y(x,t) = (1.0 mm) sin [(4.0 m^-1)x - (8.0 s^-1)t]

An incompressible liquid flows along the pipe as shown. The ratio of the speeds v₂/v₁ is:

Two notes are an "octave" apart.The ratio of their frequencies is:

The mathematical forms for the three sinusoidal traveling waves are gives by Wave 1: y(x,t) = (2 cm) sin (3x - 6t) Wave 2: y(x,t) = (3 cm) sin (4x - 12t) Wave 3: y(x,t) = (4 cm) sin (5x - 11t) Where x is in meters and t is in seconds. Of these waves:

The density of water is 1.0 g/cm³. The density of the oil in the left column of the U-tube shown below is:

When the temperature of a copper penny is increased by 100 C $\degree$ its diameter increases by 0.17%. The area of one of its faces increases by:

Which of the following represents a standing wave?

Five hoops are each pivoted at a point on the rim and allowed to swing as physical pendulums. The masses and radii are Hoop 1: M = 150g and R = 50 cm Hoop 2: M = 200g and R = 40 cm Hoop 3: M = 250g and R = 30 cm Hoop 4: M = 300g and R = 20 cm Hoop 5: M = 350g and R = 10 cm Order the hoops according to the periods of their motions, smallest to largest.

If the length of a simple pendulum is doubled, its period will:

A water line enters a house 2.0 m below ground. A smaller diameter pipe carries water to a faucet 5.0 m above ground, on the second floor. Water flows at 2.0 m/s in the main line and at 7.0 m/s on the second floor. Take the density of water to be 1.0 x10³ kg/m³. The diffenernce in pressure in the main line is 2.0 x 10⁵ Pa, then the pressure on the second floor is:

The Doppler shift formula for the frequency detected is Where ƒ ' is the frequency emitted, v is the speed of sound, v_D is the speed of the detector, and v_s is the speed of the source. Suppose the source is traveling at 5 m/s away from the detector, the detector is traveling at 7 m/s toward the source, and there is a 3 m/s wind blowing from the source toward the detector. The values that should be substituted into the Doppler shift equation are:

Object A, with heat capacity C_A and initially at temperature T_A, is placed in thermal contact with object B, with heat capacity C_B and initially at temperature T_B. The combination is thermally isolated. If the heat capacities are independent of the temperature and no phase changes occur, the final temperature of both objects is: