To find the wavelength of the stationary sound source, we can use the formula:
\[ \text{Wavelength} (\lambda) = \frac{\text{Speed of Sound}}{\text{Frequency}} \]
- Wavelength of the stationary sound source:
- Given frequency \( f = 100 \) Hz and speed of sound \( v = 1125 \) feet/second.
- Plugging in the values:
\[ \lambda = \frac{1125 \text{ ft/s}}{100 \text{ Hz}} = 11.25 \text{ ft} \]
- Perceived wavelength by the car moving toward the source:
- The perceived frequency \( f' \) can be calculated using the Doppler effect formula:
\[ f' = f \times \frac{v + v_o}{v - v_s} \]
Where:
- \( f' \) = perceived frequency
- \( f \) = emitted frequency (100 Hz)
- \( v \) = speed of sound (1125 ft/s)
- \( v_o \) = speed of the observer (car) = 100 ft/s (since the car is moving towards the source, we consider this positive)
- \( v_s \) = speed of the source = 0 ft/s (stationary source)
Plugging in the values:
\[ f' = 100 \times \frac{1125 + 100}{1125 - 0} = 100 \times \frac{1225}{1125} \approx 108.89 \text{ Hz} \]
- Now, we calculate the perceived wavelength using the new frequency:
\[ \lambda' = \frac{v}{f'} = \frac{1125 \text{ ft/s}}{108.89 \text{ Hz}} \approx 10.33 \text{ ft} \]
It seems that this perceived wavelength is not one of the options provided. Let's consider the simplest change due to movement:
Given the frequencies calculated:
- Stationary source wavelength: 11.25 ft
- Car perceived wavelength (based on the Doppler shift):
The wavelength decreases as the observer moves towards the source, making it slightly less than 11.25. Sometimes, rounding or adjustments in measurements can lead to minor variations.
The closest option that seems plausible based on our calculations for the values is likely the perceived wavelength. However, assessing the initial values can help confirm or reject the options:
From the choices:
- Wavelength of the stationary source: 11.25 ft; perceived wavelength: 10.25 ft
This is the most reasonable option given that perceived wavelengths decrease when moving toward the sound source. Therefore, resulting in:
Final answer:
- Wavelength of the stationary sound source: 11.25 ft; perceived wavelength: 10.25 ft.