Physics 20
Wave Equation Problems
1. Two waves on identical strings have frequencies in a ratio of 2 to 1. If their wave speeds are the
same, then how do their wavelengths compare?
a. 2:1
b. 1:2
c. 4:1
d. 1:4
Answer: b
2. Mac and Tosh stand 8 meters apart and demonstrate the motion of a transverse wave on a
snakey. The wave e can be described as having a vertical distance of 32 cm from a trough to a
crest, a frequency of 2.4 Hz, and a horizontal distance of 48 cm from a crest to the nearest
trough. Determine the amplitude, period, and wavelength and speed of such a wave.
Answer: Amplitude = 16 cm
(Amplitude is the distance from the rest position to the crest position which is half the vertical
distance from a trough to a crest.)
Wavelength = 96 cm
(Wavelength is the distance from crest to crest, which is twice the horizontal distance from crest
to nearest trough.)
Period = 0.42 s
(The period is the reciprocal of the frequency. T = 1 / f)
Speed = 230 cm/s
(The speed of a wave is calculated as the product of the frequency times the wavelength.)
3. Dawn and Aram have stretched a slinky between them and begin experimenting with waves. As
the frequency of the waves is doubled,
a. the wavelength is halved and the speed remains constant
b. the wavelength remains constant and the speed is doubled
c. both the wavelength and the speed are halved.
d. both the wavelength and the speed remain constant.
Answer: Answer: A
Doubling the frequency will not alter the wave speed. Rather, it will halve the wavelength.
Wavelength and frequency are inversely related.
Physics 20
4. A ruby-throated hummingbird beats its wings at a rate of about 70 wing beats per second.
a. What is the frequency in Hertz of the sound wave?
b. Assuming the sound wave moves with a velocity of 350 m/s, what is the wavelength of the wave?
Answer: Answer: f = 70 Hz and wavelength = 5.0 m
The frequency is given and the wavelength is the v/f ratio.
5. Ocean waves are observed to travel along the water surface during a developing storm. A Coast
Guard weather station observes that there is a vertical distance from high point to low point of 4.6
meters and a horizontal distance of 8.6 meters between adjacent crests. The waves splash into the
station once every 6.2 seconds. Determine the frequency
and the speed of these waves.
Answer: The wavelength is 8.6 meters and the period
is 6.2 seconds.
The frequency can be determined from the period. If T
= 6.2 s, then
f =1 /T = 1 / (6.2 s)
f = 0.161 Hz
Now find speed using the v = f • wavelength equation.
v = f • wavelength = (0.161 Hz) • (8.6 m)
v = 1.4 m/s
6. Two boats are anchored 4 meters apart. They bob up and down, returning to the same up position
every 3 seconds. When one is up the other is down. There are never any wave crests between the
boats. Calculate the speed of the waves.
Answer: The diagram is helpful. The wavelength must be 8 meters (see diagram).
The period is 3 seconds so the frequency is 1 / T or 0.333 Hz.
Physics 20
Now use speed = f • wavelength Substituting and solving for v, you will get 2.67 m/s.
7. The wavelength of a water wave in a ripple tank is 0.427m. If the frequency of the wave is
5.3Hz, what is its speed.
Answer: 2.2631 m/s
8. The distance between successive crests in a series of water waves is 4.0m, and the crests travel
9.0 m in 4.5s. What is the frequency of the waves?
Answer: 9/4.5 = 2m/s
v/wavelength= 2m/s / 4m = .5 Hz
9. The period of a sound wave from a piano is 1.18 × 10-13s. If the speed of the wave in the air is 3.4
× 102m/s, what is its wavelength?
Answer: 1/T = f = 8.475 x10
12
wavelength= v/f= 4.0118 x10
-11
10. A source with a frequency of 20Hz produces water waves that have a wavelength of 3.0cm.
What is the speed of the waves?
Answer: 20 x .030m = .6m/s