Wave Problems
Follow the steps seen in class for solving problems. If no numerical values are given, the answer should
be given in terms of symbols.
1. A stationary boat in the ocean is experiencing waves from a storm. The waves move with a
speed v and have a wavelength λ. The boat is at the crest of the wave. How much time elapses
until the boat is first at the trough of a wave?
2. Explain how you can check your answer.
3. If the waves encountered by the boat have a wavelength of 160m, and move at 56 km/h , how
much time elapses between the boat is on top of a crest and the following trough?
The motion detector used in a physics experiment sends and receives ultrasonic pulses of frequency f. A
pulse goes out, reflects of the object being measured, and returns to the detector. The sound speed in
the lab is v.
4. What is the wavelength of the waves emitted by the sensor?
5. Calculate the actual value of the wavelength when the frequency of the sensor is 40KHz and the
speed of sound, given that the room is at 20o, is 343 m/s.
6. Without using any numerical values, find the expression that can be used to determine the time
that it takes the pulse to make a round trip between the sensor and the object if the distance
between them is x.
A traveling wave has a displacement given by 𝑦𝑦(𝑥𝑥, 𝑡𝑡) = (20𝑐𝑐𝑐𝑐)cos(2𝜋𝜋𝜋𝜋 − 4𝜋𝜋𝜋𝜋), where x is measured in
cm and t in seconds. Notice that the argument of the cosine should have no units.
7. Draw a snapshot of the graph of this wave at t=0s
8. On the same set of axes, use a dotted line (----) to show the snapshot graph of a wave at
t=0.125s.
9. What is the speed of the wave?