Wave Motion 2 Question 2
2. A string $2.0 m$ long and fixed at its ends is driven by a $240 Hz$ vibrator. The string vibrates in its third harmonic mode. The speed of the wave and its fundamental frequency is
(Main 2019, 9 April II)
(a) $180 m / s, 80 Hz$
(b) $320 m / s, 80 Hz$
(c) $320 m / s, 120 Hz$
(d) $180 m / s, 120 Hz$
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Answer:
Correct Answer: 2. (b)
Solution:
- Frequency of vibration of a string in $n$th harmonic is given by
$$ f _n=n \cdot \frac{v}{2 l} $$
where, $v=$ speed of sound and $l=$ length of string.
Here, $f _3=240 Hz, l=2 m$ and $n=3$
Substituting these values in Eq. (i), we get
$\therefore 240=3 \times \frac{v}{2 \times 2} \Rightarrow v=\frac{4 \times 240}{3}=320 ms^{-1}$
Also, fundamental frequency is
$$ f=\frac{f _n}{n}=\frac{f _3}{3}=\frac{240}{3}=80 Hz $$
