a longitudinal wave with a frequency of 3.0 Hz takes 1.7 s to travel the length of a 2.5-m slinky (see figure 16.3). Determine the wavelength of the wave.

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To determine the wavelength of a wave, you need to know its speed and frequency.

The speed of a wave can be calculated using the equation:
Speed = Frequency x Wavelength

In this case, the frequency of the wave is given as 3.0 Hz, and the time it takes to travel the length of the slinky is given as 1.7 seconds. To find the speed, divide the length of the slinky by the time it takes to travel that length:

Speed = Length / Time = 2.5 m / 1.7 s = 1.47 m/s

Now, you can use the speed and frequency to calculate the wavelength. Rearrange the equation to solve for wavelength:

Wavelength = Speed / Frequency = 1.47 m/s / 3.0 Hz ≈ 0.49 m

Therefore, the wavelength of the longitudinal wave is approximately 0.49 meters.