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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.
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?
Answer
To find the frequency of vibration of the string, we first calculate the wavelength ( λ) using the formula:
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
Step 4
What is the frequency of the second harmonic?
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):
Thus, the frequency of the second harmonic is approximately 769.2 Hz.