Final answer:
The beat frequency produced by two tuning forks with wavelengths of 3.4 meters and 3.3 meters is approximately 3.0 Hz, calculated using the speed of sound and the difference between frequencies of the two sounds. The correct answer is option: E. 3.0 hertz
Step-by-step explanation:
To determine the beat frequency produced by two tuning forks with sound wavelengths of 3.4 meters and 3.3 meters, we first need to calculate the frequencies of the sounds they produce.
We can use the formula speed of sound = frequency × wavelength, where the speed of sound is approximately 343 m/s at room temperature. Let's call the frequencies of the two tuning forks f1 and f2, then:
f1 = speed of sound / wavelength 1 = 343 m/s / 3.4 m ≈ 100.88 Hz
f2 = speed of sound / wavelength 2 = 343 m/s / 3.3 m ≈ 103.94 Hz
Now, the beat frequency is determined by taking the absolute difference between the two frequencies:
Beat Frequency = |f1 - f2|
Beat Frequency = |100.88 Hz - 103.94 Hz| ≈ 3.06 Hz
Thus, the beat frequency produced is approximately 3.0 Hz, which corresponds to option E.