L05 for Physics 101

1. DOPPLER EFFECT Parly Tan L2C
Doppler Effect: The difference in frequency produced by the source and heard by the receiver with
respect to one another.
Three Cases of the Doppler effect
 Moving Source and Moving Receiver
 Moving Source and a Stationary Receiver
 Moving Receiver and Stationary Source
The frequency (Hz) of the receiver due to the Doppler Effect is given as:
𝑓𝑟 =
𝑣 ± 𝑣𝑟
𝑣 ∓ 𝑣𝑠
𝑓𝑠
where 𝑣 is 343 m/s (speed of sound in air)
𝑣𝑟 is the speed of the receiver (m/s)
𝑣𝑠 is the speed of the source (m/s)
𝑓𝑠 is the frequency of the source (Hz)
Question:
A girl hears a frequency of 600 and a boy hears a frequency of 300 Hz coming from an ice-cream truck. Is
this possible? (Assume that the truck has a frequency of 500 Hz.)
Answer:
Yes this is possible if the girl is moving towards the truck whereas the boy is moving away from the
truck.
When the receiver and the source are moving apart, the frequency heard by the receiver is lower.
When the receiver and the source are moving towards each other, the frequency heard by the receiver
is higher.

2. Moving Source and Moving Receiver
When the source and the receiver are moving towards one another, the equation above becomes
𝑓𝑟 =
𝑣 + 𝑣𝑟
𝑣 − 𝑣𝑠
𝑓𝑠
When the source and the receiver are moving away from one another, the equation above becomes
𝑓𝑟 =
𝑣 − 𝑣𝑟
𝑣 + 𝑣𝑠
𝑓𝑠
Which of the following statement is true if the speed of the receiver is increased when the source and
receiver are moving towards each other?
a) The speed of sound in the air will increase because of the addition of the receiver’s speed.
b) The speed of the source will increase because it is proportional to the speed of the receiver.
c) The frequency of the source will decrease.
d) The frequency of the receiver will increase.
Answer: C
Rationale:
The answer is not A because the speed of sound in the air is constant.
The answer is not B because the speeds of the receiver and source are independent.
The answer is not D because the frequency of the receiver will decrease according to the equation
𝑓𝑟 =
𝑣 + 𝑣𝑟
𝑣 − 𝑣𝑠
𝑓𝑠
𝑓𝑠 =
𝑣 − 𝑣𝑠
𝑣 + 𝑣𝑟
𝑓𝑟
The denominator increases and as a result, decreases the answer.
Moving Source and a Stationary Receiver
Example: A duck (moving source) swimming in water (stationary receiver)

3. 𝑓𝑟 =
𝑣 ± 𝑣𝑟
𝑣 ∓ 𝑣𝑠
𝑓𝑠
The receiver is stationary so its speed (𝑣𝑟) is 0 m/s so
𝑓𝑟 =
𝑣
𝑣 ∓ 𝑣𝑠
𝑓𝑠
For source moving towards the stationary receiver:
𝑓𝑟 =
𝑣
𝑣 − 𝑣𝑠
𝑓𝑠
For source moving away from the stationary receiver:
𝑓𝑟 =
𝑣
𝑣 + 𝑣𝑠
𝑓𝑠
Moving Receiver and Stationary Source
𝑓𝑟 =
𝑣 ± 𝑣𝑟
𝑣 ∓ 𝑣𝑠
𝑓𝑠
Waves to the right are closer (shortened) because the duck is swimming in that direction
v = fλ Therefore, the frequency is high on the right side

4. The source is stationary so its speed (𝑣𝑠) is 0 m/s so
𝑓𝑟 =
𝑣 ± 𝑣𝑟
𝑣
𝑓𝑠
For receiver moving towards the stationary source:
𝑓𝑟 =
𝑣 + 𝑣𝑟
𝑣
𝑓𝑠
For receiver moving away from the stationary source:
𝑓𝑟 =
𝑣 − 𝑣𝑟
𝑣
𝑓𝑠
Citations
Hawkes et al., (2015). Physics for Scientists and Engineers: An Interactive Approach. Toronto: Nelson
Education Ltd.
Muscovy Duck –Doppler Effect. (2008). Retrieved: February 28, 2015. From:
https://www.flickr.com/photos/sunshack/2552542952/