Practice Problems: Waves
1. I notice that every second 22 waves pass by me. What is the frequency and period of the wave?
2. I tune into my favorite FM radio station, 91.6, “Home of Ten Overplayed Songs in a Row.” If the
frequency of this station is 91.6 MHz (91.6 x 106 Hz), what is it’s wavelength? What is the period? The
speed of an electromagnetic wave is 3 x 108 m/sec.
3. As the destroyer searches for the enemy submarine, the captain pings the ocean with sonar. The speed of
sonar is 1500 m/sec in this part of the ocean. If the echo returns 4 seconds after the ping, how deep is the
submarine?
4. My new subwoofer can generate sound that has a period of 0.07 sec. What is the frequency of this wave?
What is the wavelength of this sound if the speed of sound in my room is 344 m/sec?
1. I notice that every second 22 waves pass by me. What is the frequency and period of the wave?
The number of waves that pass by in one second is the definition of frequency. So, the frequency is 22 Hz.
The period is the inverse of the frequency so
P
1
1

 0.045 seconds
f 22
2. I tune into my favorite FM radio station, 91.6, “Home of Ten Overplayed Songs in a Row.” If the
frequency of this station is 91.6 MHz (91.6 x 10 6 Hz), what is it’s wavelength? What is the period? The
speed of an electromagnetic wave is 3 x 108 m/sec.
We know that
vf
where v is the velocity of the wave, f is the frequency, and λ is the wavelength. So, let’s plug in the
numbers we are given. The frequency is 91.6 x 10 6 Hz and the velocity is 3 x 108 m/sec. So...
vf
3 x 108 m/sec   (91.6 x 106 Hz)
Divide both sides by 91.6 x 106 Hz to get
3 x 108 m/sec
91.6 x 106 Hz

91.6 x 106 Hz
91.6 x 106 Hz
3.28 m = 
The wavelength is 3.28 meters.
The period is just the inverse of the frequency so…
P
1
1

 1.09 x 10-8 seconds
6
f 91.6 x 10
3. As the destroyer searches for the enemy submarine, the captain pings the ocean with sonar. The speed of
sonar is 1500 m/sec in this part of the ocean. If the echo returns 4 seconds after the ping, how deep is the
submarine?
We know that
speed 
distance
time
In this case, the speed of the wave is 1500 m/sec and the wave returns 4 seconds after the ping. That means
it took 2 seconds to hit the submarine and 2 seconds to return to the destroyer. Plugging in values we get…
speed 
distance
time
1500 m/sec =
distance
2 seconds
multiply both sides by 2 seconds to get…
1500 m/sec (2 sec) = distance
distance = 3000 meters
4. My new subwoofer can generate sound that has a period of 0.07 sec. What is the frequency of this wave?
What is the wavelength of this sound if the speed of sound in my room is 344 m/sec?
We know that the frequency and period are inverses of each other. So…
f 
1
1

 15 Hz
P 0.07
How, we know that
vf
where v is the velocity of the wave, f is the frequency, and λ is the wavelength. So, let’s plug in the
numbers we are given. The frequency is 15 Hz and the velocity is 344 m/sec. So...
vf
344 m/sec   (15 Hz)
Divide both sides 15 Hz to get
344 m/sec

15 Hz
λ = 22.9 meters
Your subwoofer creates waves that are 75 feet long!