Advertisements
Advertisements
Question
Discuss the following case-
Observer in motion and Source at rest.
- Observer moves towards Source
- Observer resides away from the Source
Advertisements
Solution
(a) Observer moves towards Source:
Observer moves towards Source
We can assume that the observer O moves towards the source S with velocity vo. The source S is at rest and the velocity of sound waves (with respect to the medium) produced by the source is v.
From the Figure, It is observed that both vo and v are in opposite direction. Then, their relative velocity is vr = v + vo. The wavelength of the sound wave is λ = `"v"/"f"`, which means the frequency observed by the observer O is f ‘ = `"v"_"r"/lambda`. Then
`"f"' = "v"_"r"/lambda = (("v" + "v"_0)/"v")"f"`
`= "f"(1 + "v"_0/"v")` ...(7)
(b) Observer recedes away from the Source:
If the observer O is moving away (receding away) from the source S, then velocity v0 and v move in the same direction. Hence, their relative velocity is vr = v – v0. Hence, the frequency observed by the observer O is
`"f"' = "v"_"r"/lambda = (("v" + "v"_0)/"v")"f"`
`= "f"(1 - "v"_0/"v")` ...(8)
APPEARS IN
RELATED QUESTIONS
In discussing Doppler effect, we use the word "apparent frequency". Does it mean that the frequency of the sound is still that of the source and it is some physiological phenomenon in the listener's ear that gives rise to Doppler effect? Think for the observer approaching the source and for the source approaching the observer.
State the expression for apparent frequency when listener is stationary and source is moving towards the listener.
A ship in a sea sends SONAR waves straight down into the seawater from the bottom of the ship. The signal reflects from the deep bottom bedrock and returns to the ship after 3.5 s. After the ship moves to 100 km it sends another signal which returns back after 2 s. Calculate the depth of the sea in each case and also compute the difference in height between two cases.
Two cars moving in opposite directions approach each other with speed of 22 m/s and 16.5 m/s respectively. The driver of the first car blows a horn having a frequency 400 Hz. The frequency heard by the driver of the second car is [velocity of sound 340 m/s]: ____________.
The difference between the apparent frequency of a stationary 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 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.
In a quink tube experiment, a tuning fork of frequency 300 Hz is vibrated at one end. It is observed that intensity decreases from maximum to 50% of its maximum value, as tube is moved by 6.25 cm. Velocity of sound is ______ m/s.
When a sound source of frequency n is approaching a stationary observer with velocity u than the apparent change in frequency is Δn1 and when the same source is receding with velocity u from the stationary observer than the apparent change in frequency is Δn2. Then ______.
When an engine passes near to a stationary observer then its apparent frequencies occurs in the ratio 5/3. If the velocity of engine is ______.
A whistle producing sound waves of frequencies 9500 Hz and above is approaching a stationary person with speed v ms-1. The velocity of sound in air is 300 ms-1. If the person can hear frequencies up to a maximum of 10,000 HZ, the maximum value of v up to which he can hear the whistle is ______.
