A hiker shouts towards a vertical cliff 465 m away. The echo is heard 2.75 s. later. The wavelength of the sound is 0.750 m. What is its frequency?
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To find the frequency of the sound, we need to use the formula:
Frequency = Speed / Wavelength
First, we need to find the speed of sound. The speed of sound in air at normal conditions is approximately 343 meters per second.
Next, we can calculate the time it took for the sound to travel to the cliff and back as follows:
Since the sound traveled a distance of 465 m to reach the cliff and then another 465 m back, the total distance traveled is 2 * 465 m = 930 m.
Given that the time taken is 2.75 s, we can calculate the speed of sound as Distance / Time = 930 m / 2.75 s = 338.1818 m/s (rounded to four decimal places).
Now, we can substitute the values into the formula:
Frequency = Speed / Wavelength
Frequency = 338.1818 m/s / 0.750 m = 450.9091 Hz (rounded to four decimal places).
Therefore, the frequency of the sound is approximately 450.9091 Hz.