UBC Phys 101

1. The Doppler Effect
Question 1: Define what is meant by the Doppler Effect.
Question 2: You are sitting outside enjoying the sunshine and reading a book when a small
child starts running towards you screaming. If the child is screaming at a very annoying
frequency of 9800 Hz, and running in a speed of 9.5km/h, what is the frequency at which you
hear the screams? (Speed of sound in air is approximately 343m/s)
Frequency = __________Hz
Question 3: The child runs past you, and is now running away from you at the same speed
and still screaming at the same frequency. What is the frequency you hear now?
Frequency = __________Hz
Question 4: You give up reading and start walking home at a speed of 5km/h. As you walk on
the sidewalk, you hear a fire truck approaching because someone burned popcorn again and
set off the fire alarm. If fire truck sirens are at a frequency of 2500 Hz, and you are hearing it
at a frequency of 2670 Hz, how fast is the fire truck moving towards you? (v=343m/s)
Speed = __________km/h

2. Solutions
Question 1
The Doppler Effect is the phenomenon where there is an increase or decrease in frequency of a
wave as the source, receiver, or both move towards or away from each other.
Question 2
The equation for the Doppler Effect is the following:
𝑓𝑟 =
𝑣 ± 𝑣𝑟
𝑣 ∓ 𝑣𝑠
𝑓𝑠
We are given that v=343m/s, vs=9.5km/h and fs=9800Hz. As you are sitting on a chair, we can
assume vr=0m/s. In order to have the same units, we must convert 9.5km/h into m/s:
𝑣𝑠 =
9.5
3.6
= 2.64𝑚/𝑠
As the source is moving towards the receiver, the top sign on the equation is used. Plugging the
values into the equation we get:
𝑓𝑟 =
343𝑚/𝑠 + 0𝑚/𝑠
343𝑚/𝑠 − 2.64𝑚/𝑠
× 9800𝐻𝑧 = 9876𝐻𝑧
Question 3
As the values are the same as the previous question, the only thing that changes in this case is
the sign of the equation. As the source of the sound is now moving away from the receiver, we
use the bottom sign of the equation. Plugging the values into the equation we get:
𝑓𝑟 =
343𝑚/𝑠 − 0𝑚/𝑠
343𝑚/𝑠 + 2.64𝑚/𝑠
× 9800𝐻𝑧 = 9725𝐻𝑧
Question 4
In this question we are asked to find vs, therefore we will first rearrange the Doppler Effect
equation in order to solve for that. As in this question the source and the receiver are moving
towards each other, we will use the top sign in the equation.
𝑓𝑟 =
𝑣 + 𝑣𝑟
𝑣 − 𝑣𝑠
𝑓𝑠

3. 𝑓𝑟(𝑣 − 𝑣𝑠)
𝑓𝑠
= 𝑣 + 𝑣𝑟
𝑣 − 𝑣𝑠 =
(𝑣 + 𝑣𝑟)𝑓𝑠
𝑓𝑟
𝑣𝑠 = 𝑣 −
(𝑣 + 𝑣𝑟)𝑓𝑠
𝑓𝑟
Now that we have rearranged the equation we may plug in values. From the question we know
that v=343m/s, vr=5km/h, fs=2500Hz, and fr=2670Hz. Once again, we must convert 5km/h into
m/s:
5
3.6
= 1.39𝑚/𝑠
Plugging in all the values we get:
𝑣𝑠 = 343𝑚/𝑠 −
(343𝑚/𝑠 + 1.39𝑚/𝑠) × 2500𝐻𝑧
2670𝐻𝑧
= 20.5𝑚/𝑠
To convert to km/h:
20.5 × 3.6 = 73.8𝑘𝑚/ℎ