Wave Motion 2 Question 19
19. A sonometer wire resonates with a given tuning fork forming standing waves with five antinodes between the two bridges when a mass of $9 kg$ is suspended from the wire. When this mass is replaced by mass $M$. The wire resonates with the same tuning fork forming three antinodes for the same positions of the bridges. The value of $M$ is
$(2002,2 M)$
(a) $25 kg$
(b) $5 kg$
(c) $12.5 kg$
(d) $1 / 25 kg$
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Answer:
Correct Answer: 19. (a)
Solution:
- Let $f _0=$ frequency of tuning fork
Then, $f _0=\frac{5}{2 l} \sqrt{\frac{9 g}{\mu}} \quad(\mu=$ mass per unit length of wire $)$
$$ =\frac{3}{2 l} \sqrt{\frac{M g}{\mu}} $$
Solving this, we get $M=25 kg$
In the first case, frequency corresponds to fifth harmonic while in the second case it corresponds to third harmonic.
