# Worksheet: Modeling One-Dimensional Transverse Waves

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

**Q2: **

A wave is modelled with the function , where is measured in meters and is measured in seconds.

What is the wave’s amplitude?

What is the wave’s wave number?

What is the wave’s angular frequency?

What is the wave’s speed?

What is the phase shift of the wave?

- A rad
- B rad
- C rad
- D rad
- E rad

What is the wave’s wavelength?

What is the wave’s period?

**Q4: **

A motorboat is traveling across a lake at a speed of 15 m/s. Waves are propagating on the lake, and the boat bounces up and down when it passes a wave. The boat bounces up and down every 0.5 s while moving in the same direction that the waves propagate, and it bounces up and down every 0.3 s while moving in the opposite direction opposite to the propagation of the waves.

What is the speed of the waves? Give your answer to one decimal place.

What is the wavelength of the waves? Give your answer to one decimal place.

**Q9: **

Two sinusoidal waves, which are identical except for a phase shift, travel along in the same direction. The wave equation of the resultant wave is

What is the angular frequency?

What is the wave number?

What amplitude do the waves both have?

What is the phase difference between the waves?

- A rad
- B rad
- C rad
- D rad
- E rad

**Q15: **

AM radio has a frequency range of 540 kHz to 1,600 kHz, while FM radio has a frequency range of 88.0 MHz to 108 MHz.

Calculate the wavelength range for AM radio.

- A191 m to 542 m
- B187 m to 556 m
- C196 m to 636 m
- D178 m to 535 m
- E181 m to 652 m

Calculate the wavelength range for FM radio.

- A2.67 m to 3.30 m
- B2.83 m to 3.66 m
- C2.31 m to 3.42 m
- D2.78 m to 3.41 m
- E2.21 m to 3.02 m

**Q18: **

A computer user finds that his wireless router transmits data at a rate of 75 Mbps (megabits per second).

How much time is required for the router to transmit a single bit of data?

- A s
- B s
- C s
- D s
- E s

If a reflected wifi signal has to travel 8.00 m further than a directly received wifi signal, what will be the time difference between receiving the direct signal and the reflected signal?

- A s
- B s
- C s
- D s
- E s

**Q19: **

A pulse can be described as a single wave disturbance that moves through a medium. Consider a pulse that is defined at time s by the equation , centered around m. The pulse moves with a velocity m/s in the positive -direction.

What is the amplitude of the pulse?

What value of is the pulse centered around when s?

**Q23: **

Consider two sinusoidal waves traveling along a string modeled as and , where is measured in meters and in seconds. The resultant of these waves can be found using .

What is the wave number of the resultant wave?

- A4 m
^{−1} - B3 m
^{−1} - C5 m
^{−1} - D0.8 m
^{−1} - E10 m
^{−1}

What is the angular frequency of the resultant wave?