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:

  1. 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

$$ f=\frac{f _n}{n}=\frac{f _3}{3}=\frac{240}{3}=80 Hz $$



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