Wave: 9 m wavelength, 5 s period. Speed?

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Question

What is the defining equation for the speed (v) of a wave in terms of its wavelength (λ) and period (T)?

Answer

v = λ / T. Speed equals wavelength divided by period.

Question

A wave has a wavelength of 9 meters and a period of 5 seconds. Calculate its speed. What is its frequency in Hertz (Hz)?

Answer

Speed = 1.8 m/s (v = 9 m / 5 s = 1.8 m/s). Frequency = 0.2 Hz (f = 1/T = 1/5 s = 0.2 Hz).

Question

How are frequency (f) and period (T) of a wave mathematically related? If the period of a wave is 0.1 seconds, what is its frequency?

Answer

They are reciprocals: f = 1/T and T = 1/f. For T = 0.1 s, f = 1/0.1 = 10 Hz.

Question

If the wavelength of a wave is doubled while its frequency is held constant, what happens to its speed?

Answer

The speed doubles. Since v = fλ, if f is constant and λ doubles, v also doubles.

Question

A water wave travels at 3 m/s and has a frequency of 0.5 Hz. What is its wavelength?

Answer

λ = v / f = 3 m/s / 0.5 Hz = 6 meters.

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Is the speed of a wave calculated by dividing its wavelength by its period?

The wave’s speed is 1.8 m/s.