The difference between the apparent frequency of a source of sound as ...
Is it 3m/s...n1=n(v/v-vs).n2=n(v/v+vs).n1-n2=nv[1/v-vs - 1/v+vs].n1-n2=nv[ V+Vs-V+Vs/V^2-Vs^2].n1-n2=2n VVs/V^2-Vs^2.2 n /100=2 n VVs/V^2-Vs^2.1/100=300×Vs/(300 ^2 -Vs^2).9×10^4-Vs^2=3×10^4Vs.-Vs^2 - 3×10^4Vs + 9× 10^4 .take roots ...we get 3
The difference between the apparent frequency of a source of sound as ...
Introduction:
The apparent frequency of a source of sound as perceived by a stationary observer depends on the relative motion between the observer and the source. When the source is approaching the observer, the apparent frequency is higher than the actual frequency, and when the source is receding from the observer, the apparent frequency is lower.
Given:
- The difference between the apparent frequency during approach and recession is 2% of the actual frequency.
- The speed of sound is 300 m/s.
Calculating the Speed of the Source:
Let's assume the actual frequency of the source is 'f' Hz. During approach, the apparent frequency is higher, so it will be 'f + 0.02f = 1.02f' Hz. During recession, the apparent frequency is lower, so it will be 'f - 0.02f = 0.98f' Hz.
To calculate the speed of the source, we need to use the Doppler effect equation for sound waves:
v = (f_a - f_s) / (f_a + f_s) * c
Where:
- v is the speed of the source
- f_a is the apparent frequency
- f_s is the actual frequency
- c is the speed of sound in the medium
Calculating the Speed of the Source during Approach:
Substituting the values into the Doppler effect equation during approach:
v_approach = (1.02f - f) / (1.02f + f) * 300
Calculating the Speed of the Source during Recession:
Substituting the values into the Doppler effect equation during recession:
v_recession = (0.98f - f) / (0.98f + f) * 300
Equating the Two Equations:
Since the difference between the apparent frequencies during approach and recession is 2% of the actual frequency, we can set up the following equation:
v_approach - v_recession = 0.02f
Substituting the expressions for v_approach and v_recession:
[(1.02f - f) / (1.02f + f) * 300] - [(0.98f - f) / (0.98f + f) * 300] = 0.02f
Solving for the Speed of the Source:
Simplifying the equation:
[(1.02f - f) - (0.98f - f)] / (1.02f + f - 0.98f - f) * 300 = 0.02f
Simplifying further:
0.04f / (0.04f) * 300 = 0.02f
300 = 0.02f
f = 15000 Hz
Now, substituting the value of f back into either of the equations for v_approach or v_recession will give us the speed of the source.
Conclusion:
The speed of the source of sound is determined to be 15000 Hz.
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