Question:
A siren emitting sound of frequency 800 Hz is going away from a static listener with a speed of 30 m/s. Frequency of sound heard by the listener is (Velocity of sound in air = 340 m/s)
A siren emitting sound of frequency 800 Hz is going away from a static listener with a speed of 30 m/s. Frequency of sound heard by the listener is (Velocity of sound in air = 340 m/s)
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To remember the signs in the Doppler formula, think logically. If the source and listener are moving closer, the frequency should increase (so make the numerator larger and/or the denominator smaller). If they are moving apart, the frequency should decrease (so make the numerator smaller and/or the denominator larger).
Updated On: Jul 1, 2026
- 286.5 Hz
- 418.2 Hz
- 733.3 Hz
- 644.5 Hz
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The Correct Option is C
Solution and Explanation
Step 1: Understanding the Question:
This is a problem on the Doppler effect for sound waves. The sound source is moving away from a stationary listener, and we need to find the apparent frequency heard by the listener.
Step 2: Key Formula or Approach:
The general formula for the Doppler effect is:
\[ f' = f \left( \frac{v \pm v_L}{v \mp v_S} \right) \]
where \(f'\) is the apparent frequency, \(f\) is the source frequency, \(v\) is the speed of sound, \(v_L\) is the speed of the listener, and \(v_S\) is the speed of the source.
In our case:
- The listener is static, so \(v_L = 0\).
- The source is moving
away from the listener. This should cause the apparent frequency to decrease. To make the fraction smaller, we use a '+' sign in the denominator.
So the formula becomes:
\[ f' = f \left( \frac{v}{v + v_S} \right) \]
Step 3: Detailed Explanation:
We are given the following values:
- Source frequency, \(f = 800\) Hz.
- Speed of sound, \(v = 340\) m/s.
- Speed of the source, \(v_S = 30\) m/s.
Substitute these values into the formula:
\[ f' = 800 \left( \frac{340}{340 + 30} \right) \]
\[ f' = 800 \left( \frac{340}{370} \right) \]
\[ f' = 800 \times \frac{34}{37} \]
\[ f' = \frac{27200}{37} \approx 735.13 \text{ Hz} \]
This value is closest to 733.3 Hz. The small discrepancy might be due to rounding in the problem's intended answer or a slightly different value for the speed of sound used. 733.3 Hz is the most plausible answer.
Let's re-calculate with 733.3 Hz as the target. \(800 * (340/370) = 735.13...\). \(800 * (330/360) = 733.33\). It seems the problem might have intended to use v=330m/s. However, based on the given values, 735.13 Hz is the calculated answer, and 733.3 Hz is the closest option.
Step 4: Final Answer:
The frequency of sound heard by the listener is approximately 733.3 Hz.
This is a problem on the Doppler effect for sound waves. The sound source is moving away from a stationary listener, and we need to find the apparent frequency heard by the listener.
Step 2: Key Formula or Approach:
The general formula for the Doppler effect is:
\[ f' = f \left( \frac{v \pm v_L}{v \mp v_S} \right) \]
where \(f'\) is the apparent frequency, \(f\) is the source frequency, \(v\) is the speed of sound, \(v_L\) is the speed of the listener, and \(v_S\) is the speed of the source.
In our case:
- The listener is static, so \(v_L = 0\).
- The source is moving
away from the listener. This should cause the apparent frequency to decrease. To make the fraction smaller, we use a '+' sign in the denominator.
So the formula becomes:
\[ f' = f \left( \frac{v}{v + v_S} \right) \]
Step 3: Detailed Explanation:
We are given the following values:
- Source frequency, \(f = 800\) Hz.
- Speed of sound, \(v = 340\) m/s.
- Speed of the source, \(v_S = 30\) m/s.
Substitute these values into the formula:
\[ f' = 800 \left( \frac{340}{340 + 30} \right) \]
\[ f' = 800 \left( \frac{340}{370} \right) \]
\[ f' = 800 \times \frac{34}{37} \]
\[ f' = \frac{27200}{37} \approx 735.13 \text{ Hz} \]
This value is closest to 733.3 Hz. The small discrepancy might be due to rounding in the problem's intended answer or a slightly different value for the speed of sound used. 733.3 Hz is the most plausible answer.
Let's re-calculate with 733.3 Hz as the target. \(800 * (340/370) = 735.13...\). \(800 * (330/360) = 733.33\). It seems the problem might have intended to use v=330m/s. However, based on the given values, 735.13 Hz is the calculated answer, and 733.3 Hz is the closest option.
Step 4: Final Answer:
The frequency of sound heard by the listener is approximately 733.3 Hz.
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