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Zorluk: ZorWaves, Sound, and Light

A sound wave generated in air enters a pool of water, where its propagation speed increases by a factor of four. How are the frequency and wavelength of the sound wave affected upon entering the water?

  1. A
    The frequency quadruples, while the wavelength remains unchanged.
  2. The frequency remains unchanged, while the wavelength quadruples.Cevap
  3. C
    The frequency remains unchanged, while the wavelength is reduced to one-fourth.
  4. D
    Both the frequency and the wavelength double.

Cevap

The frequency remains unchanged, while the wavelength quadruples.
When any wave crosses the boundary between two media, its frequency is conserved because frequency is determined solely by the source vibration. According to the wave equation v=fλv = f\lambda, if wave speed increases by a factor of 4 while frequency remains constant, the wavelength must also increase by a factor of 4 to maintain the equality.

Adım Adım Çözüm

1
Identify the behavior of wave frequency across a boundary.
The frequency (ff) remains constant because it depends exclusively on the oscillating source.
When a wave transitions from one medium into another, particles at the boundary oscillate in synchronization with the incident wave, preserving frequency.
2
Apply the universal wave equation relating speed, frequency, and wavelength.
v=fλv = f\lambda, which rearranges to λ=vf\lambda = \frac{v}{f}.
This formula defines the relationship between the physical parameters of any wave.
3
Calculate the proportional change in wavelength when speed increases by a factor of 4.
Since vwater=4vairv_{\text{water}} = 4v_{\text{air}} and ff is constant, λwater=4vairf=4λair\lambda_{\text{water}} = \frac{4v_{\text{air}}}{f} = 4\lambda_{\text{air}}.
Wavelength is directly proportional to wave speed when frequency is constant.

Anahtar Kavram

Wave boundary behavior and the wave equation (v=fλv = f\lambda)
Tahmini Süre:1m 0s
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Konular

Waves, Sound, and Light

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