Step 1: Understanding the Doppler Effect for a Moving Observer
When the sound source is not moving and the observer moves toward it, the frequency they hear increases.
When the observer moves away from the stationary source, the frequency they hear decreases.
Step 2: Writing the Frequency Formulas
If the actual frequency of the source is
n, the speed of sound is
v, and the observer's speed is
u :
When moving toward the source:
n1=n(‌)When moving away from the source:
n2=n(‌)Step 3: Using the Ratio Given in the Problem
We are told that the ratio of the two frequencies is
n1:n2=71:65. We set up an equation:
‌=‌=‌Step 4: Solving for Observer's Speed
(u)Cross-multiply the equation:
65(v+u)=71(v−u)Expand:
65v+65u=71v−71uMove both
v terms to one side and
u terms to the other:
65u+71u=71v−65v136u=6vDivide both sides by 136 :
u=‌=‌Step 5: Substitute Speed of Sound Value
The speed of sound is
v=340m∕s.
Plug this value into the formula for
u:u=‌=‌=15m∕sTo change
15m∕s into
km∕h, multiply by
‌:15×‌=54km∕h
