# Worksheet: Modeling Longitudinal Waves

In this worksheet, we will practice using amplitude, wave number, angular frequency, and phase shift to model the motion of a longitudinal wave.

**Q1: **

A graph of a compression wave, as shown in the accompanying diagram, shows snapshots of the wave’s function at the instants (shown by the blue line) and (shown by the red line) respectively. In evaluating the characteristics of the pressure wave, use three significant figure precision.

What is the wavelength of the compression wave?

What is the magnitude of the maximum displacement of the compression wave?

What is the speed of the compression wave?

What is the period of the compression wave?

**Q3: **

A speaker is placed at the opening of a long horizontal tube. The speaker oscillates, creating a sound wave that moves through the tube at a speed of 340 m/s. The sound wave is modeled with the wave function , where is measured in meters and is measured in seconds. At time , an air molecule at the position is at the maximum displacement of 7.00 nm. At the same time, another molecule at the position has a displacement of 3.00 nm. What is the frequency at which the speaker is oscillating?

**Q5: **

A speaker is placed at the opening of a long horizontal tube. The speaker oscillates, creating a sound wave that moves down the tube. The wave moves through the tube at a speed of 340 m/s. The sound wave is modeled with the wave function . At time , an air molecule at the point is at the maximum displacement . At , another air molecule that is at the point has a displacement of 2.30 nm.

What is the wave number of the wave?

What is the angular frequency of the wave?

What is the initial phase angle of the wave?

**Q8: **

The displacement of certain gas molecules in a sound wave is modeled with the wave function , where is measured in meters and in seconds.

What is the speed of the sound wave?

What is the maximum speed of the air molecules as they oscillate in simple harmonic motion?

- A m/s
- B m/s
- C m/s
- D m/s
- E m/s

What is the magnitude of the maximum acceleration of the air molecules as they oscillate in simple harmonic motion?

**Q10: **

A wave traveling on a Slinky that is 5.0 m in length takes 2.8 s to travel the length of the Slinky and back again.

What is the speed of the wave?

Using the same Slinky stretched to the same length, a standing wave is created which consists of three antinodes and four nodes. At what frequency must the Slinky be oscillating?