QUARTER FINAL STAGE 2024
Accra Academy: 45 points
Oyoko Methodist SHS: 36 points
St. Joseph Seminary SHS: 28 points
ROUND 2 - SPEED RACE
THIRD QUESTION
The middle of a stretched string fixed between two posts 2 meters apart is plucked gently.
Find the wavelength of the fundamental mode of the subsequent vibration of the string.
ANSWER: $\lambda = 4 \text{ m}$
FORMULA
$\lambda = 2L$
SOLUTION:
$\lambda = 2 \times 2$
$\lambda = 4 \text{ m}$
ANSWER: $\lambda = 4 \text{ m}$
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PRACTICE QUESTIONS
1. QUESTION: The middle of a stretched string fixed between two posts 1.5 m apart is plucked gently. Find the wavelength of the fundamental mode of vibration.
ANSWER: 3.0 m
SOLUTION:
$\lambda = 2L$ (fundamental: half a wavelength fits the string)
$\lambda = 2 \times 1.5$
$\lambda = 2 \times 15\times10^{-1}$
$\lambda = 3.0\text{ m}$
2. QUESTION: The middle of a stretched string fixed between two posts 0.80 m apart is plucked gently. Find the wavelength of the fundamental mode of vibration.
ANSWER: 1.6 m
SOLUTION:
$\lambda = 2L$ (fundamental: half a wavelength fits the string)
$\lambda = 2 \times 0.80$
$\lambda = 2 \times 8\times10^{-1}$
$\lambda = 1.6\text{ m}$
3. QUESTION: The middle of a stretched string fixed between two posts 1.2 m apart is plucked gently. Find the wavelength of the fundamental mode of vibration.
ANSWER: 2.4 m
SOLUTION:
$\lambda = 2L$ (fundamental: half a wavelength fits the string)
$\lambda = 2 \times 1.2$
$\lambda = 2 \times 12\times10^{-1}$
$\lambda = 2.4\text{ m}$
4. QUESTION: The middle of a stretched string fixed between two posts 0.65 m apart is plucked gently. Find the wavelength of the fundamental mode of vibration.
ANSWER: 1.3 m
SOLUTION:
$\lambda = 2L$ (fundamental: half a wavelength fits the string)
$\lambda = 2 \times 0.65$
$\lambda = 2 \times 65\times10^{-2}$
$\lambda = 1.3\text{ m}$
5. QUESTION: The middle of a stretched string fixed between two posts 3.5 m apart is plucked gently. Find the wavelength of the fundamental mode of vibration.
ANSWER: 7.0 m
SOLUTION:
$\lambda = 2L$ (fundamental: half a wavelength fits the string)
$\lambda = 2 \times 3.5$
$\lambda = 2 \times 35\times10^{-1}$
$\lambda = 7.0\text{ m}$
6. QUESTION: The middle of a stretched string fixed between two posts 0.45 m apart is plucked gently. Find the wavelength of the fundamental mode of vibration.
ANSWER: 0.90 m or $9.0\times10^{-1}$ m
SOLUTION:
$\lambda = 2L$ (fundamental: half a wavelength fits the string)
$\lambda = 2 \times 0.45$
$\lambda = 2 \times 45\times10^{-2}$
$\lambda = 0.90\text{ m}$
7. QUESTION: The middle of a stretched string fixed between two posts 1.8 m apart is plucked gently. Find the wavelength of the fundamental mode of vibration.
ANSWER: 3.6 m
SOLUTION:
$\lambda = 2L$ (fundamental: half a wavelength fits the string)
$\lambda = 2 \times 1.8$
$\lambda = 2 \times 18\times10^{-1}$
$\lambda = 3.6\text{ m}$
8. QUESTION: The middle of a stretched string fixed between two posts 0.35 m apart is plucked gently. Find the wavelength of the fundamental mode of vibration.
ANSWER: 0.70 m or $7.0\times10^{-1}$ m
SOLUTION:
$\lambda = 2L$ (fundamental: half a wavelength fits the string)
$\lambda = 2 \times 0.35$
$\lambda = 2 \times 35\times10^{-2}$
$\lambda = 0.70\text{ m}$
9. QUESTION: The middle of a stretched string fixed between two posts 4.5 m apart is plucked gently. Find the wavelength of the fundamental mode of vibration.
ANSWER: 9.0 m
SOLUTION:
$\lambda = 2L$ (fundamental: half a wavelength fits the string)
$\lambda = 2 \times 4.5$
$\lambda = 2 \times 45\times10^{-1}$
$\lambda = 9.0\text{ m}$