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Zorluk: KolayWave Properties and Mathematical Wave Equation

A periodic water wave of frequency 5.0 Hz5.0\text{ Hz} has a wavelength of 1.2 m1.2\text{ m} in deep water. When the wave enters a shallow section of the ripple tank, its speed reduces to 4.0 m s−14.0\text{ m s}^{-1}. What is the wavelength of the wave in the shallow section?

  1. A
    0.67 m0.67\text{ m}
  2. 0.80 m0.80\text{ m}Cevap
  3. C
    1.5 m1.5\text{ m}
  4. D
    1.8 m1.8\text{ m}

Cevap

0.80 m0.80\text{ m}
When a wave travels from one medium to another (e.g., deep to shallow water), its frequency ff remains constant because frequency is dependent only on the wave source. Using the wave equation v=fλv = f\lambda, the wavelength in the shallow water is calculated as λ=vf=4.0 m s−15.0 Hz=0.80 m\lambda = \frac{v}{f} = \frac{4.0\text{ m s}^{-1}}{5.0\text{ Hz}} = 0.80\text{ m}.

Adım Adım Çözüm

1
Determine the invariant property across media boundaries
The frequency ff remains constant at 5.0 Hz5.0\text{ Hz} when a wave passes from deep water to shallow water.
Frequency is determined solely by the source of the wave vibration, not the medium of propagation.
2
Calculate the wavelength in the shallow section using the wave equation
λ2=v2f=4.0 m s−15.0 Hz=0.80 m\lambda_2 = \frac{v_2}{f} = \frac{4.0\text{ m s}^{-1}}{5.0\text{ Hz}} = 0.80\text{ m}
Applying the relationship v=fλv = f\lambda for the second medium.

Anahtar Kavram

Frequency invariance of waves across boundaries and application of the wave equation v=fλv = f\lambda
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Konular

Wave Properties and Mathematical Wave Equation

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