A stationary source produces a sound wave at a frequency of 100 Hz. The wave travels at 1125 feet per second. A car is moving toward the sound source at a speed of 100 feet per second. What is the wavelength of the stationary sound source and the wavelength that a person in the car perceives?
First, we need to calculate the wavelength of the sound wave produced by the stationary source:
The formula to calculate wavelength is:
\[
\text{Wavelength} = \dfrac{\text{Speed of sound}}{\text{Frequency}}
\]
Given that the speed of sound is 1125 feet per second and the frequency is 100 Hz, we can calculate the wavelength of the stationary sound source as:
\[
\text{Wavelength} = \dfrac{1125 \text{ ft/s}}{100 \text{ Hz}} = 11.25 \text{ ft}
\]
Now, we need to calculate the perceived wavelength of the sound wave by a person in the car:
The formula to calculate the perceived wavelength due to the Doppler effect is:
\[
\text{Perceived Wavelength} = \dfrac{\text{Speed of sound in air} + \text{Speed of observer}}{\text{Speed of sound in air}} \times \text{Wavelength of stationary source}
\]
Given that the speed of sound in air is 1125 feet per second, the speed of the observer (car) is moving towards the source at 100 feet per second, and the wavelength of the stationary source is 11.25 feet, we can calculate the perceived wavelength as:
\[
\text{Perceived Wavelength} = \dfrac{1125 \text{ ft/s} + 100 \text{ ft/s}}{1125 \text{ ft/s}} \times 11.25 \text{ ft} = \dfrac{1225 \text{ ft/s}}{1125 \text{ ft/s}} \times 11.25 \text{ ft} = 12.22 \text{ ft}
\]
Therefore, the wavelength of the stationary sound source is 11.25 feet, and the perceived wavelength by a person in the car is 12.22 feet.