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Zorluk: KolayWave Phenomena: Reflection, Refraction, Interference, Diffraction, and Polarization

Two sound waves of frequencies 440 Hz440\text{ Hz} and 445 Hz445\text{ Hz} travel through air and superpose to produce beats. What is the resulting beat frequency, in hertz?

Cevap: 5 Hz

Cevap

The beat frequency produced by the superposition of the two sound waves is 5 Hz5\text{ Hz}.
When two waves of slightly different frequencies interfere, periodic variations in sound intensity called beats occur. The number of beats heard per second is equal to the absolute difference between the frequencies of the two superposing waves: fbeat=∣f2−f1∣=∣445 Hz−440 Hz∣=5 Hzf_{\text{beat}} = |f_2 - f_1| = |445\text{ Hz} - 440\text{ Hz}| = 5\text{ Hz}.

Adım Adım Çözüm

1
Identify the frequencies of the interfering waves
f1=440 Hzf_1 = 440\text{ Hz} and f2=445 Hzf_2 = 445\text{ Hz}
Beat frequency is determined by the absolute difference between the individual wave frequencies.
2
Subtract the lower frequency from the higher frequency to find the beat frequency
fbeat=∣445−440∣=5 Hzf_{\text{beat}} = |445 - 440| = 5\text{ Hz}
The rate of periodic intensity variation (beat frequency) is governed by fbeat=∣f2−f1∣f_{\text{beat}} = |f_2 - f_1|.

Anahtar Kavram

Beat Frequency and Wave Superposition
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Konular

Wave Phenomena: Reflection, Refraction, Interference, Diffraction, and Polarization

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