PHYS 221 SI Worksheet
1. An ambulance is behind your car and you are both going in the same direction in still air. The
ambulance is going at a speed of 30 m/s and its siren emits a tone at 400 Hz. The frequency that you
hear is 390 Hz. How fast are you going in your car? (The speed of sound in air is 340 m/s.)
2. A guitar string 50 cm long with a mas 10 g is vibrating in its third harmonic and emits a frequency of
600 Hz. What is the tension if the string?
3. A surveyor uses a steel (α = 1.2E-5 K-1) measuring tape that is exactly 50.000 m long at a
temperature of 20°C. What is its length on a hot summer day when the temperature is 35°C? If a value
of 35.794 is read off the tape on this hot day, what is the actual distance? Assume that the tape is
calibrated for use at 20°C. (Hint: if the tape is longer on the hot day, is the distance measured greater
than or less than the actual distance? You can use this and a ratio of lengths to find the actual length.)
4. An aluminum (Y = 7.0E10 Pa and α = 2.4E-5 K-1) cylinder 10 cm long, with a cross-sectional area of
20 cm2, is to be used as a spacer between two steel walls. At 17.2 °C it just slips between the walls.
When it warms to 22.3 °C, calculate the stress in the cylinder and the total force it exerts on each wall,
assuming the walls are perfectly rigid and a constant distance apart.