The frequency of a stretched string depends on its length. Give two other factors that affect the frequency of a stretched string. The diagram shows a guitar string stretched between supports 0.65 m apart. The string is vibrating at its first harmonic. The speed of sound in the string is 500 m s⁻¹. What is the frequency of vibration of the string? Draw a diagram of the string when it vibrates at its second harmonic. What is the frequency of the second harmonic?

Leaving Cert Physics Vibration & Sound: The frequency of a stretched str

The frequency of a stretched string depends on its length - Leaving Cert Physics - Question 12(c) - 2005

Question 12(c)

The frequency of a stretched string depends on its length. Give two other factors that affect the frequency of a stretched string. The diagram shows a guitar string... show full transcript

Worked Solution & Example Answer:The frequency of a stretched string depends on its length - Leaving Cert Physics - Question 12(c) - 2005

Step 1

Give two other factors that affect the frequency of a stretched string.

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Answer

The frequency of a stretched string depends on several factors:

Tension: Increasing the tension in the string increases its frequency.
Linear Density: The mass per unit length of the string affects its frequency; a denser string will have a lower frequency.

Step 2

What is the frequency of vibration of the string?

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Answer

To find the frequency of vibration of the string, we first calculate the wavelength ( λ) using the formula:

$λ = 2L = 2 imes 0.65 ext{ m} = 1.3 ext{ m}$

Next, we use the wave speed formula: v = fλ, where v is the speed of sound in the string and f is the frequency.

Rearranging gives us: f = \frac{v}{λ} = \frac{500 ext{ m/s}}{1.3 ext{ m}} ≈ 384.6 ext{ Hz}.

Step 3

Draw a diagram of the string when it vibrates at its second harmonic.

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Answer

The diagram for the string vibrating at its second harmonic will show two loops. The nodes are at each end and there is one antinode in the middle:

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Step 4

What is the frequency of the second harmonic?

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Answer

The frequency of the second harmonic can be calculated using the formula: f_{n} = nf_{1}, where n is the harmonic number and f₁ is the fundamental frequency. For the second harmonic (n = 2):

$f_{2} = 2f_{1} = 2 imes 384.6 ext{ Hz} = 769.2 ext{ Hz}.$

Thus, the frequency of the second harmonic is approximately 769.2 Hz.

The frequency of a stretched string depends on its length - Leaving Cert Physics - Question 12(c) - 2005

Worked Solution & Example Answer:The frequency of a stretched string depends on its length - Leaving Cert Physics - Question 12(c) - 2005

Give two other factors that affect the frequency of a stretched string.

What is the frequency of vibration of the string?

Draw a diagram of the string when it vibrates at its second harmonic.

What is the frequency of the second harmonic?

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