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rain that is approaching with a speed of 50.0 m/s due North, sounding a 740 Hz horn. What quency sound do you hear? Take the speed of sound in air= 342 m/s.

rain that is approaching with a speed of 50.0 m/s due North, sounding a 740 Hz horn. What quency sound do you hear? Take the speed of sound in air= 342 m/s.

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### Doppler Shift Problem **Question:** You are driving with a speed of 40.0 m/s due South, head-on towards a train that is approaching with a speed of 50.0 m/s due North, sounding a 740 Hz horn. What frequency sound do you hear? Take the speed of sound in air as 342 m/s. **Explanation:** The Doppler Effect is the change in frequency or wavelength of a wave in relation to an observer who is moving relative to the wave source. In this scenario, both the observer (you) and the source (the train) are moving towards each other, which results in an observed frequency higher than the emitted frequency. To calculate the observed frequency (\( f' \)), the following formula is used: \[ f' = f \left( \frac{v + v_0}{v - v_s} \right) \] Where: - \( f' \) is the observed frequency - \( f \) is the emitted frequency (740 Hz) - \( v \) is the speed of sound in the medium (342 m/s) - \( v_0 \) is the speed of the observer (40.0 m/s) - \( v_s \) is the speed of the source (50.0 m/s) ### Calculation: \[ f' = 740 \left( \frac{342 + 40}{342 - 50} \right) \] ### Answer: The exact observed frequency \( f' \) can be calculated by plugging in the values. *Note: Perform the calculation using a calculator or a software for precision.*
Transcribed Image Text:### Doppler Shift Problem **Question:** You are driving with a speed of 40.0 m/s due South, head-on towards a train that is approaching with a speed of 50.0 m/s due North, sounding a 740 Hz horn. What frequency sound do you hear? Take the speed of sound in air as 342 m/s. **Explanation:** The Doppler Effect is the change in frequency or wavelength of a wave in relation to an observer who is moving relative to the wave source. In this scenario, both the observer (you) and the source (the train) are moving towards each other, which results in an observed frequency higher than the emitted frequency. To calculate the observed frequency (\( f' \)), the following formula is used: \[ f' = f \left( \frac{v + v_0}{v - v_s} \right) \] Where: - \( f' \) is the observed frequency - \( f \) is the emitted frequency (740 Hz) - \( v \) is the speed of sound in the medium (342 m/s) - \( v_0 \) is the speed of the observer (40.0 m/s) - \( v_s \) is the speed of the source (50.0 m/s) ### Calculation: \[ f' = 740 \left( \frac{342 + 40}{342 - 50} \right) \] ### Answer: The exact observed frequency \( f' \) can be calculated by plugging in the values. *Note: Perform the calculation using a calculator or a software for precision.*
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