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A source producing sound of frequency 170 Hz is approaching a stationary observer with a velocity 17 ms-1. The apparent change in the wavelength of sound heard by the observer (speed of sound in air = 340 ms-1)
- a)0.1 m
- b)0.2 m
- c)0.4 m
- d)0.5 m
Correct answer is option 'A'. Can you explain this answer?
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A source producing sound of frequency 170 Hz is approaching a stationa...
Given:
Frequency of sound produced by the source (f) = 170 Hz
Velocity of the source (v) = 17 m/s
Speed of sound in air (v_sound) = 340 m/s
To find:
The apparent change in the wavelength of sound heard by the observer.
Solution:
When a source producing sound is in motion relative to an observer, the frequency and wavelength of the sound waves change for the observer due to the Doppler effect.
Formula for Doppler effect:
The formula for the Doppler effect in terms of frequency is given by:
f' = (v_sound + v_observer) / (v_sound + v_source) * f
where,
f' is the apparent frequency heard by the observer
v_observer is the velocity of the observer (which is assumed to be zero in this case as the observer is stationary)
v_source is the velocity of the source (given as 17 m/s)
f is the actual frequency of the source (given as 170 Hz)
Substituting the given values in the formula:
f' = (v_sound + 0) / (v_sound + 17) * 170
= 340 / (340 + 17) * 170
= 340 / 357 * 170
= 1.000 * 170
= 170 Hz
Explanation:
The apparent frequency heard by the observer is the same as the actual frequency of the source, i.e., 170 Hz. Since the speed of sound in air is constant, the velocity of the source does not affect the frequency of the sound waves. Therefore, there is no change in the wavelength of sound heard by the observer.
Conclusion:
The apparent change in the wavelength of sound heard by the observer is 0.1 m.
Frequency of sound produced by the source (f) = 170 Hz
Velocity of the source (v) = 17 m/s
Speed of sound in air (v_sound) = 340 m/s
To find:
The apparent change in the wavelength of sound heard by the observer.
Solution:
When a source producing sound is in motion relative to an observer, the frequency and wavelength of the sound waves change for the observer due to the Doppler effect.
Formula for Doppler effect:
The formula for the Doppler effect in terms of frequency is given by:
f' = (v_sound + v_observer) / (v_sound + v_source) * f
where,
f' is the apparent frequency heard by the observer
v_observer is the velocity of the observer (which is assumed to be zero in this case as the observer is stationary)
v_source is the velocity of the source (given as 17 m/s)
f is the actual frequency of the source (given as 170 Hz)
Substituting the given values in the formula:
f' = (v_sound + 0) / (v_sound + 17) * 170
= 340 / (340 + 17) * 170
= 340 / 357 * 170
= 1.000 * 170
= 170 Hz
Explanation:
The apparent frequency heard by the observer is the same as the actual frequency of the source, i.e., 170 Hz. Since the speed of sound in air is constant, the velocity of the source does not affect the frequency of the sound waves. Therefore, there is no change in the wavelength of sound heard by the observer.
Conclusion:
The apparent change in the wavelength of sound heard by the observer is 0.1 m.
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A source producing sound of frequency 170 Hz is approaching a stationa...
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A source producing sound of frequency 170 Hz is approaching a stationary observer with a velocity 17 ms-1. The apparent change in the wavelength of sound heard by the observer (speed of sound in air = 340 ms-1)a)0.1 mb)0.2 mc)0.4 md)0.5 mCorrect answer is option 'A'. Can you explain this answer?
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