Question

In a physics demonstration, Mr. H establishes a standing wave pattern in a snakey (Long spring) by vibranting it up and down with 32 vibrations in 10 seconds. Gerald is holding the opposite end of the snakey and it’s standing 6.2m from Mr.H’s end. There are 4 equal length sections in the snakey, each occupied by an antinode. Determine the frequency, wavelength, and speed of the wave.

Answer 1

Answer on Question 73453, Physics, Other

Question:

In a physics demonstration, Mr. H establishes a standing wave pattern in a snakey (long spring) by vibrating it up and down with 32 vibrations in 10 seconds. Gerald is holding the opposite end of the snakey and it's standing $6.2m$ from Mr.H's end. There are 4 equal length sections in the snakey, each occupied by an antinode. Determine the frequency, wavelength, and speed of the wave.

Solution:

a) The frequency can be found as follows:

$$f = \frac {3 2 \text {vibrations}}{1 0 \text {seconds}} = 3. 2 \mathrm {Hz}.$$

b) In the picture below we can see the standing wave pattern in the long string:

As we can see from the picture there are 5 nodes (depicted as N) and 4 antinodes (depicted as AN) in a distance of $6.2m$ . Also, we can see from the picture that there are four loops. One complete wave in a standing wave pattern consists of two loops. Therefore, the length of the string is equal to two wavelengths of the wave:

$$L = \frac {1}{2} n \lambda = \frac {4}{2} \lambda = 2 \lambda ,$$

here, $L = 6.2 \, m$ is the length of the string, $n = 4$ is the number of the loops, $\lambda$ is the wavelength.

Then, from this formula we can find the wavelength of the wave:

$$\lambda = \frac {L}{2} = \frac {6 . 2 m}{2} = 3. 1 m.$$

c) We can find the speed of the wave from the wave speed formula:

$$v = f \lambda,$$

here, $v$ is the speed of the wave, $f = 3.2\, \text{Hz}$ is the frequency and $\lambda = 3.1\, \text{m}$ is the wavelength.

Let's substitute the numbers:

$$v = f \lambda = 3.2\, \text{Hz} \cdot 3.1\, \text{m} = 9.92\, \text{ms}^{-1}.$$

Answer:

a) $f = 3.2\, \text{Hz}$

b) $\lambda = 3.1\, \text{m}$

c) $v = 9.92\, \text{ms}^{-1}$

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