To find the frequency of the sound, we first need to determine the speed of sound using the time it takes for the echo to return.
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Calculate the total distance the sound travels: Since the hiker is shouting towards a cliff and waiting for the echo to come back, the sound travels to the cliff and then back to the hiker. Thus, the total distance traveled by the sound is: \[ \text{Total Distance} = 2 \times \text{Distance to Cliff} = 2 \times 481 , \text{m} = 962 , \text{m} \]
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Determine the speed of sound: The total time for the echo to return is 3.0 seconds. Therefore, the speed of sound can be calculated as: \[ \text{Speed of Sound} = \frac{\text{Total Distance}}{\text{Time}} = \frac{962 , \text{m}}{3.0 , \text{s}} \approx 320.67 , \text{m/s} \]
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Calculate the frequency using the relationship between speed, frequency, and wavelength: The formula relating speed (v), frequency (f), and wavelength (λ) is: \[ v = f \times \lambda \] Rearranging for frequency gives: \[ f = \frac{v}{\lambda} \] Substituting the calculated values into this equation: \[ f = \frac{320.67 , \text{m/s}}{0.9 , \text{m}} \approx 356.3 , \text{Hz} \]
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Select the closest answer choice: The closest answer to 356.3 Hz in the provided options is 357 Hz.
Therefore, the frequency of the sound is approximately 357 Hz.
1 answer