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CGP EDU Academic Team
Published on: September 12, 2026
The apparent frequency is n, when a source of sound approaches a stationary listener with a velocity X. It is n 2 when the listener approaches the stationary source with equal speed X. Then n 1 > n 2 .
Text Solution
Verified by ExpertsThe correct answer is:
A
Step 1: When the source of sound approaches a stationary listener, the observed frequency increases due to the Doppler effect. The formula for the observed frequency when the source moves towards the listener is given by:
n = n_0 \left( \frac{v}{v - v_s} \right)
where n_0 is the actual frequency, v is the speed of sound, and v_s is the speed of the source.
Step 2: Since the source is moving towards the listener, the velocity of the source is positive (v_s = X). Thus, we have:
n_1 = n_0 \left( \frac{v}{v - X} \right)
Step 3: When the listener approaches a stationary source with speed X, the frequency observed by the listener is:
n_2 = n_0 \left( \frac{v + v_l}{v} \right)
where v_l is the speed of the listener (v_l = X). So we have:
n_2 = n_0 \left( \frac{v + X}{v} \right)
Step 4: Now let's analyze both expressions. We can say that:
n_1 = n_0 \left( \frac{v}{v - X} \right) and n_2 = n_0 \left( \frac{v + X}{v} \right)
Step 5: Comparing both frequencies:
Since v > v - X, it implies n_1 > n_0. The term (v/(v - X)) will be greater than (v + X)/v as the numerator of n_1 is higher compared to its denominator's reduction effect. Therefore, we conclude that n_1 > n_2.
Thus, we find that n_1 > n_2 holds true.
n = n_0 \left( \frac{v}{v - v_s} \right)
where n_0 is the actual frequency, v is the speed of sound, and v_s is the speed of the source.
Step 2: Since the source is moving towards the listener, the velocity of the source is positive (v_s = X). Thus, we have:
n_1 = n_0 \left( \frac{v}{v - X} \right)
Step 3: When the listener approaches a stationary source with speed X, the frequency observed by the listener is:
n_2 = n_0 \left( \frac{v + v_l}{v} \right)
where v_l is the speed of the listener (v_l = X). So we have:
n_2 = n_0 \left( \frac{v + X}{v} \right)
Step 4: Now let's analyze both expressions. We can say that:
n_1 = n_0 \left( \frac{v}{v - X} \right) and n_2 = n_0 \left( \frac{v + X}{v} \right)
Step 5: Comparing both frequencies:
Since v > v - X, it implies n_1 > n_0. The term (v/(v - X)) will be greater than (v + X)/v as the numerator of n_1 is higher compared to its denominator's reduction effect. Therefore, we conclude that n_1 > n_2.
Thus, we find that n_1 > n_2 holds true.
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