Let's break down the problem step by step.

Given:

• Length of the string, $L = 20 \, \text{cm} = 0.20 \, \text{m}$
• Number of complete waves that fit along the string, $n = 4$
• Frequency of the oscillator, $f = 30 \, \text{Hz}$

(a) What is their wavelength?

The total length of the string is 20 cm, and 4 complete waves fit along this length. To find the wavelength, we use the fact that the length of the string is equal to the number of wavelengths:

$\text{Wavelength} (\lambda) = \frac{\text{Length of the string}}{\text{Number of waves}} = \frac{L}{n}$

Substituting the known values:

$\lambda = \frac{0.20 \, \text{m}}{4} = 0.05 \, \text{m}$

So, the wavelength of the waves is 0.05 m.

(b) What is their frequency?

The problem already gives the frequency of the oscillator, which is the same as the frequency of the waves traveling along the string. The frequency $f$ is:

$f = 30 \, \text{Hz}$

So, the frequency is 30 Hz.

(c) What is their speed?

To find the speed of the waves, we use the formula:

$v = f \times \lambda$

Substituting the known values:

$v = 30 \, \text{Hz} \times 0.05 \, \text{m} = 1.5 \, \text{m/s}$

So, the speed of the waves on the string is 1.5 m/s.

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Summary of answers:

(a) The wavelength of the waves is 0.05 m.
(b) The frequency of the waves is 30 Hz.
(c) The speed of the waves is 1.5 m/s.

Would you like further explanation on any of these points?

Here are some related questions you might find interesting:

1. How does changing the frequency affect the wavelength on the string?
2. How can we calculate the speed of sound in a medium like air using similar principles?
3. What would happen to the speed of the waves if the tension in the string were increased?
4. What is the relationship between the wavelength, frequency, and speed of waves in different media?
5. How does the number of complete waves on the string change if the string length were increased?

Tip: Increasing the tension on a stretched string increases the speed of waves traveling on it!