Advertisements
Advertisements
Question
Discuss the following case-
Both are in motion
- Source and Observer approach each other
- Source and Observer resides from each other
- Source chases Observer
- Observer chases Source
Advertisements
Solution
(a) Source and observer approach each other:
Let vs and vo be the respective velocities of source and observer approaching each other as shown in Figure. In order to calculate the apparent frequency observed by the observer, let us have a dummy (behaving as observer or source) in between the source and observer. Since the dummy is at rest, the dummy (observer) observes the apparent frequency due to the approaching source as given in equation f ‘ = `"f"/((1 - "v"_"s"/"v"))`
`"f"_"d" = "f"/((1 - "v"_"s"/"v"))` ....(1)
The true observer approaches the dummy from the other side at that instant of time. Since the source (true source) comes in a direction opposite to the true observer, the dummy (source) is treated as a stationary source for the true observer at that instant. Hence, apparent frequency when the true observer approaches the stationary source (dummy source), f’ = `"f"(1 + "v"_0/"v")`.
f’ = `"f"_"d"(1 + "v"_0/"v")`
`=> "f"_"d" = "f'"/((1 + "v"_0/"v"))` ....(2)
Since this is true for any arbitrary time, therefore, comparing equation (1) and equation (2), we get
`"f"/((1 - "v"_"s"/"v")) = "f'"/((1 + "v"_0/"v"))`
`=> "vf'"/(("v + v"_0)) = "vf"/(("v - v"_s))`
Hence, the apparent frequency as seen by the observer is
`"f'" = (("v" + "v"_0)/("v" -"v"_"s"))"f"` ....(3)
(b) Source and observer recede from each other:
It is noticed that the velocity of the source and the observer each point in opposite directions with respect to the case in (a) and hence, we substitute (vs → – vs) and (v0 → – v0) in equation (3), and therefore, the apparent frequency observed by the observer when the source and observer recede from each other is f’ = `(("v" - "v"_0)/("v" + "v"_"s"))"f"`
(c) Source chases the observer:
Only the observer’s velocity is oppositely directed when compared to case (a). Therefore, substituting (v0 → – v0) in equation (3), we get f’ = `(("v" - "v"_0)/("v" - "v"_"s"))"f"`
(d) Observer chases the source:
Only the source velocity is oppositely directed when compared to case (a). Therefore, substituting (vs → – vs) in equation (3), we get f’ =
= `(("v" + "v"_0)/("v" + "v"_"s"))"f"`
APPEARS IN
RELATED QUESTIONS
A narrow sound pulse (for example, a short pip by a whistle) is sent across a medium. (a) Does the pulse have a definite (i) frequency, (ii) wavelength, (iii) speed of propagation? (b) If the pulse rate is 1 after every 20 s, (that is the whistle is blown for a split of second after every 20 s), is the frequency of the note produced by the whistle equal to 1/20 or 0.05 Hz
Solve the following problem.
A police car travels towards a stationary observer at a speed of 15 m/s. The siren on the car emits a sound of frequency 250 Hz. Calculate the recorded frequency. The speed of sound is 340 m/s.
A sound source and listener are both stationary and a strong wind is blowing. Is there a Doppler effect?
The difference between the apparent frequency of a source of sound as perceived by the observer during its approach and recession is 2% of the frequency of the source. If the speed of sound in air is 300 ms-1, then the velocity of the source is ______.
A source of sound is moving towards a stationary observer with velocity 'Vs' and then moves away with velocity 'Vs'. Assume that the medium through which the sound waves travel is at rest, if 'V' is the velocity of sound and 'n' is the frequency emitted by the source, then the difference between the apparent frequencies heard by the observer is ______.
A train, standing in a station yard, blows a whistle of frequency 400 Hz in still air. The wind starts blowing in the direction from the yard to the station with a speed of 10 m/s. Given that the speed of sound in still air is 340 m/s ______.
- the frequency of sound as heard by an observer standing on the platform is 400 Hz.
- the speed of sound for the observer standing on the platform is 350 m/s.
- the frequency of sound as heard by the observer standing on the platform will increase.
- the frequency of sound as heard by the observer standing on the platform will decrease.
The frequency of echo will be ______ Hz if the train blowing a whistle of frequency 320 Hz is moving with a velocity of 36 km/h towards a hill from which an echo is heard by the train driver. The velocity of sound in air is 330 m/s.
The observer is moving with velocity 'v0' towards the stationary source of sound and then after crossing moves away from the source with velocity 'v0'. Assume that the medium through which the sound waves travel is at rest. If v is the velocity of sound and n is the frequency emitted by the source, then the difference between apparent frequencies heard by the observer is ______.
When an observer moves towards a stationary source with velocity 'V₁', the apparent frequency of emitted note is 'F₁'. When observer moves away from stationary source with velocity 'V₁' the appearent frequency is 'F2'. If 'v' is velocity of sound in air and \[\frac {F_1}{F_2}\] = 2, then \[\frac {V}{V_1}\] is equal to ______.
The pitch of whistle of an engine appears to drop by 30% of the original value when it passes a stationary observer. If speed of sound in air is 350 m/s, then the speed of engine in m/s is ______.
