a source of sound id traveling towards a stationary observer .The frequency of sound is heard by the observer is 25% more that the actual frequency.If the speed of sound is v,that of the source is
options:
1.v/4
2.v/5
Heloo ashu...the answer is v/4 bcoz :-
let the first frequency be v1 and the second be v2.it is give that v2 is 25% of v1 i.e.
V2
We can use the formula for the Doppler effect to solve this problem. The formula is given by:
f' = (v + vo) / (v + vs) * f
Where:
f' is the observed frequency
v is the speed of sound
vo is the velocity of the observer
vs is the velocity of the source
f is the actual frequency
In this case, the observer is stationary, so the velocity of the observer (vo) is 0. The observed frequency (f') is 25% more than the actual frequency (f), which means f' = 1.25f.
Plugging in these values into the formula, we get:
1.25f = (v + 0) / (v + vs) * f
Simplifying the equation, we get:
1.25 = v / (v + vs)
Now, let's solve for vs, the velocity of the source:
1.25(v + vs) = v
1.25v + 1.25vs = v
1.25vs = v - 1.25v
1.25vs = 0.25v
vs = 0.25v / 1.25
Simplifying further, we get:
vs = 0.2v
So, the velocity of the source is 0.2 times the speed of sound (v/5).
Therefore, the correct option is 2. v/5.
To find the speed of the source, we need to use the formula for the Doppler effect. The Doppler effect is the change in frequency or wavelength of a wave in relation to an observer who is moving relative to the wave source.
In this case, the source of sound is traveling towards a stationary observer. The frequency of sound heard by the observer is 25% more than the actual frequency. Let's denote the actual frequency as f and the observed frequency as f'.
The formula for the Doppler effect when the source is moving towards the observer is:
f' = (v + vo) / (v) * f
Where:
- f' is the observed frequency
- f is the actual frequency
- v is the speed of sound
- vo is the speed of the source (which we need to find)
Given that the observed frequency is 25% more than the actual frequency, we can write:
f' = 1.25f
Substituting these values into the Doppler effect formula, we have:
1.25f = (v + vo) / (v) * f
Simplifying the equation, we can cancel out the 'f' terms:
1.25 = (v + vo) / (v)
Next, we can cross multiply to get rid of the fraction:
(v + vo) = 1.25v
Expanding the equation:
v + vo = 1.25v
Now, we can isolate the vo term:
vo = 1.25v - v
Simplifying further:
vo = 0.25v
Therefore, the speed of the source is v/4. So, the correct option is 1. v/4.