Wave 20 m/s, λ = 4 m. Frequency?

A
5 s⁻¹

B
16 s⁻¹

C
24 s⁻¹

D
80 s⁻¹

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Question

A sound wave travels from air into a denser medium like water. Its speed and wavelength both change. What happens to its frequency? Why?

Answer

Its frequency remains constant. Frequency is determined by the source and does not change when the wave enters a new medium; only the speed and wavelength adjust to satisfy v = fλ.

Question

If a wave's speed is doubled while its wavelength is held constant, how does the frequency change? What if the speed is constant and the wavelength is doubled?

Answer

1) If speed doubles (v' = 2v) and λ is constant, then f' = v'/λ = 2v/λ = 2f (frequency doubles). 2) If speed is constant and λ doubles, then f' = v/(2λ) = f/2 (frequency halves).

Question

The wave equation v = fλ is fundamental. What are the units for each variable in the SI system, and how does this ensure dimensional consistency in the equation?

Answer

v in m/s, f in Hz (1/s or s⁻¹), λ in m. Therefore, (m/s) = (1/s) × (m), which is dimensionally consistent.

Question

An ocean wave has a wavelength of 40 m and a frequency of 0.1 Hz. What is its speed? How does this compare to the speed of a radio wave (an electromagnetic wave) of the same frequency?

Answer

v_water = fλ = 0.1 Hz × 40 m = 4 m/s. A radio wave of 0.1 Hz would travel at c ≈ 3×10⁸ m/s (the speed of light in a vacuum). Same frequency, vastly different speeds and wavelengths because they are different types of waves.

Question

For a standing wave on a string fixed at both ends, the fundamental frequency is given by f = v/(2L), where L is the string length. If you want to double this fundamental frequency, what are two distinct ways you could adjust the string's physical properties (consider v = √(Tension/μ))?

Answer

1) Halve the length L (f ∝ 1/L). 2) Quadruple the tension T (since v ∝ √T, and f ∝ v, so f ∝ √T; to double f, you need v to double, which requires T to quadruple).

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For all types of waves (sound, light, water), does the relationship v = fλ hold true?

Wave 20 m/s, λ = 4 m. Frequency?

A
5 s⁻¹

B
16 s⁻¹

C
24 s⁻¹

D
80 s⁻¹

The frequency of the wave is 5 s⁻¹ (5 Hz).

Topic Flashcards

Mini Quiz

Related Questions

Wave 20 m/s, λ = 4 m. Frequency?

A 5 s⁻¹ B 16 s⁻¹ C 24 s⁻¹ D 80 s⁻¹

The frequency of the wave is 5 s⁻¹ (5 Hz).

Topic Flashcards

Mini Quiz

Related Questions

A
5 s⁻¹

B
16 s⁻¹

C
24 s⁻¹

D
80 s⁻¹